ISSN 00418994
eISSN: 22402926

Forthcoming Articles
(Last update: November 12, 2019)
The following articles will soon be published in this journal.
Their publication status can be :

online first – final version available;

accepted – manuscript available.
Click on the title to view the paper.

Abdollahi, Alireza and Taheri, Zahra publication status: accepted

Yan, Quanfu and Shen, Zhencai publication status: accepted

Bosi A.A. and Facchini A. publication status: accepted

Nguyen, Huu Tri Nhat and Tran, Ngoc Hoi publication status: accepted

Blache, Regis publication status: accepted

Mantegazza, Carlo publication status: accepted

Ho, KwokPun publication status: accepted

HernandezMada, Genaro publication status: accepted

Tirado Hernandez, Maria de la Paz
publication status: accepted

Mahatab, K. publication status: accepted

Filimonova A.R., Vorob'ev N.N. and Yang N.
publication status: accepted

Zhang, Bin publication status: accepted

Holubowski, Waldemar and Macedonska, Olga publication status: accepted

Lewintan, P. publication status: accepted

Abedi, Mostafa and Estaji, Ali Akbar publication status: accepted

Positselski, L. publication status: accepted

Luyen, D.T. publication status: accepted

Alexandru V., Achimescu S. and Andronescu C.S. publication status: accepted

Albrecht, Ulrich and McQuaig, Bradley publication status: accepted

Greenberg, M. and Seveso, M.A. publication status: online first

Sharaf, K. publication status: online first
Manuscripts of the accepted Papers
 Abdollahi, Alireza and Taheri, Zahra
Abstract: A famous conjecture about group algebras of torsionfree groups states that there is no zero divisor in such group algebras. A recent approach to settle the conjecture is to show the nonexistence of zero divisors with respect to the length of possible ones, where by the length we mean the size of the support of an element of the group algebra. The case length $2$ cannot be happen. The first unsettled case is the existence of zero divisors of length $3$.
Here we study possible length $3$ zero divisors in the rational group algebras and in the group algebras over the field $\mathbb{F}_p$ with $p$ elements for some prime $p$.
As a consequence we prove that the rational group algebras of torsionfree groups which are residually finite $p$group for some prime $p\neq 3$ have no zero divisor of length $3$. We note that the determination of all zero divisors of length $3$ in group algebras over $\mathbb{F}_2$ of cyclic groups is equivalent to find all trinomials (polynomials with 3 nonzero terms) divided by irreducible polynomials over $\mathbb{F}_2$. The latter is a subject studied in coding theory and we add here some results, e.g. we show that $1+x+x^2$ is a zero divisor in the group algebra over $\mathbb{F}_2$ for some element $x$ of the group if and only if $x$ is of finite order divided by $3$ and we find all $\beta$ in the group algebra of the shortest length such that $(1+x+x^2)\beta=0$; and $1+x^2+x^3$ or $1+x+x^3$ is a zero divisor in the group algebra over $\mathbb{F}_2$ for some element $x$ of the group if and only if $x$ is of finite order divided by $7$. received 09.12.2018, accepted 04.11.2019 (14 pages)
download: manuscript (294K)
 Yan, Quanfu and Shen, Zhencai
Abstract: Let $G$ be a finite group and ${\mathcal{F}}$ be a nonempty formation. We define the ${\mathcal{F}^*}$norm, denoted by $N_{\mathcal{F}}^{*}(G)$, to be intersection of the normalizers of the ${\mathcal{F}}$residuals of all $F$subgroups of $G$, where $F={\mathcal{N}}{\mathcal{F}}$ is the class of all groups whose ${\mathcal{F}}$residuals are nilpotent. In this paper, we research the properties of $N_{\mathcal{F}}^{*}(G)$ and investigate the relationship between $N_{\mathcal{F}}^{*}(G)$ and $N_{\mathcal{F}}(G),$ where $N_{\mathcal{F}}(G)$ is the intersection of the normalizers of the ${\mathcal{F}}$residuals of all subgroups of $G.$ We show that $N_{\mathcal{F}}^{*}(G)=N_{\mathcal{F}}(G)$ if ${\mathcal{A}}\subseteq {\mathcal{F}}\subseteq{\mathcal{N}}.$ received 21.06.2018, accepted 28.10.2019 (10 pages)
download: manuscript (234K)
 Bosi A.A. and Facchini A.
Abstract:
A ringed partially ordered set with zero is a pair $(L, F)$, where $L$
is a partially ordered set with a least element $0_L$ and $F\colon
L\to\mathbf{Ring}$ is a covariant functor. Here the partially ordered set $L$ is
given a category structure in the usual way and $\mathbf{Ring}$ denotes the
category of associative rings with identity. Let $\mathbf{RingedParOrd}_0$ be
the category of ringed partially ordered sets with zero. There is a
functor $\mathcal{H}\colon\mathbf{Ring}\to\mathbf{RingedParOrd}_0$ that associates to any ring
$R$ a ringed partially ordered set with zero $(Hom(R), F_R)$. The
functor $\mathcal{H}$ has a left inverse $Z\colon\mathbf{RingedParOrd}_0\to\mathbf{Ring}$. The
category $\mathbf{RingedParOrd}_0$ is a fibred category.
received 27.02.2019, accepted 28.10.2019 (10 pages)
download: manuscript (313K)
 Nguyen, Huu Tri Nhat and Tran, Ngoc Hoi
Abstract: Let $R$ be a unital subring of a commutative ring $S,$ which is a free $R$module of rank $m.$ In 1994 and then in 2017, V. A. Koibaev and we described normalizers of subgroups $GL(n, S)$ and $E(n, S)$ in $G = GL(mn, R)$, and showed that they are equal and coincide with the set $\{g \in G: E(n, S)^g \leq GL(n, S)\} = Aut(S/R) \ltimes GL(n, S).$\mathcal{H}reover, for any proper ideal A of R, $$N_{G}(E(n, S)E(mn, R, A)) = \rho_{A}^{1}(N_{GL(mn, R/A)}(E(n, S/SA))).$$ In the present paper, we prove similar results about normalizers of classical subgroups, namely, the normalizers of subgroups $EO(n, S), SO(n, S), O(n, S)$ and $GO(n,S)$ in $G$ are equal and coincide with the set $\{g \in G: EO(n, S)^g \leq GO(n, S)\} = Aut(S/R) \ltimes GO(n, S).$ Similarly, the ones of subgroups $Ep(n, S),$\\ $Sp(n, S)$ and $GSp(n, S)$ are equal and coincide with the set $\{g \in G: Ep(n, S)^g \leq GSp(n, S)\} = Aut(S/R) \ltimes GSp(n, S).$
Moreover, for any proper ideal $A$ of $R,$
$$N_{G}(EO(n, S)E(mn, R, A)) = \rho_{A}^{1}(N_{GL(mn, R/A)}(EO(n, S/SA)))$$ and
$$N_{G}(Ep(n, S)E(mn, R, A)) = \rho_{A}^{1}(N_{GL(mn, R/A)}(Ep(n, S/SA))).$$
When $R = S,$ we obtain the known results of N. A. Vavilov and V. A. Petrov. received 18.10.2018, accepted 10.10.2019 (13 pages)
download: manuscript (282K)
 Blache, Regis
Abstract:
In a classical paper, Manin gives a congruence [15, Theorem 1]
for the characteristic polynomial of the action of Frobenius on the
Jacobian of a curve $C$, defined over the finite field $\mathbf{F}_{q}$,
$q=p^m$, in terms of its HasseWitt matrix.
The aim of this article is to prove a congruence similar to Manin's one,
valid for any $L$function $L(f,T)$ associated to the exponential sums
over affine space attached to an additive character of $\mathbf{F}_q$, and a
polynomial $f$. In order to do this, we define a HasseWitt matrix
$\mathrm{HW}(f)$, which depends on the characteristic $p$, the set $D$ of
exponents of $f$, and its coefficients.
We also give some applications to the study of the Newton polygon of
ArtinSchreier (hyperelliptic when $p=2$) curves, and zeta functions of
varieties.
received 21.03.2019, accepted 04.10.2019 (21 pages)
download: manuscript (561K)
 Mantegazza, Carlo
Abstract: We discuss some elementary questions in the calculus of variations related to the Lavrentiev phenomenon and the uniqueness of the minimizers. received 17.07.2019, accepted 27.09.2019 (6 pages)
download: manuscript (366K)
 Ho, KwokPun
Abstract: We establish the boundedness of the Erd\'{e}lyiKober fractional integral operators on ball Banach function spaces. In particular, it gives the boundedness of the Erd\'{e}lyiKober fractional integral operators on amalgam spaces and Morrey spaces. received 23.07.2019, accepted 10.09.2019 (14 pages)
download: manuscript (316K)
 HernandezMada, Genaro
Abstract: We give a criterion for the good reduction of semistable $K3$ surfaces over $p$adic fields. We use neither $p$adic Hodge theory nor transcendental methods as in the analogous proofs of criteria for good reduction of curves or $K3$ surfaces. We achieve our goal by realizing the special fiber $X_s$ of a semistable model $X$ of a $K3$ surface over the $p$adic field $K$, as a special fiber of a logfamily in characteristic $p$ and use an arithmetic version of the ClemensSchmid exact sequence in order to obtain a KulikovPerssonPinkham classification theorem in characteristic $p$. received 23.04.2019, accepted 27.08.2019 (20 pages)
download: manuscript (333K)
 Tirado Hernandez, Maria de la Paz
Abstract: We describe the module of integrable derivations in the sense of
HasseSchmidt of the quotient of the polynomial ring in two
variables over an ideal generated by the equation
$x^ny^q$. received 08.01.2019, accepted 08.07.2019 (12 pages)
download: manuscript (351K)
 Mahatab, K.
Abstract: We estimate the number of composite elements in the $n$th grade of a group semiring of finite boolean groups. In view of this result
we conjecture that the composites in these semirings of finite groups are thinly dispersed. received 15.08.2018, accepted 02.07.2019 (6 pages)
download: manuscript (246K)
 Zhang, Bin
Abstract: It is well known that all of the prime cyclotomic polynomials and binary cyclotomic polynomials are flat,
and the flatness of ternary cyclotomic polynomials is much more complicated.
Let $p received 23.03.2019, accepted 01.07.2019 (19 pages)
download: manuscript (417K)
 Holubowski, Waldemar and Macedonska, Olga
Abstract: Let $G$ be a finitely generated relatively free group that is locally graded. We show that either $G$ contains a nontrivial free subsemigroup or $G$ is nilpotentbyfinite. received 30.05.2018, accepted 17.06.2019 (5 pages)
download: manuscript (161K)
 Lewintan, P.
Abstract: In this paper we considerably extend the class of known $\alpha$minimizing hypercones using subcalibration methods. Indeed, the improvement of previous results follows from a careful analysis of special cubic and quartic polynomials. received 29.10.2018, accepted 31.05.2019 (20 pages)
download: manuscript (349K)
 Abedi, Mostafa and Estaji, Ali Akbar
Abstract: For a completely regular frame $L$, the ring $\mathcal{R}L$ of realvalued continuous functions on $L$ is equipped with the uniform topology.
The closed ideals of $\mathcal{R}L$ in this topology are studied, and a new, merely algebraic characterization of these ideals is given.
This result is used to describe the real ideals of $\mathcal{R}L$, and to characterize pseudocompact frames and Lindelöf frames.
It is shown that a frame $L$ is finite if and only if every ideal of $\mathcal{R}L$ is closed.
Finally, we prove that every closed ideal in $\mathcal{R}L$ is an intersection of maximal ideals. received 31.01.2018, accepted 30.04.2019 (18 pages)
download: manuscript (319K)
 Positselski, L.
Abstract: The definition of a pseudodualizing complex is obtained from that
of a dualizing complex by dropping the injective dimension
condition, while retaining the finite generatedness and homothety
isomorphism conditions.
In the specific setting of a pair of associative rings, we show that
the datum of a pseudodualizing complex induces a triangulated
equivalence between a pseudocoderived category and
a pseudocontraderived category.
The latter terms mean triangulated categories standing in between
the conventional derived category and the coderived or
the contraderived category.
The constructions of these triangulated categories use appropriate
versions of the Auslander and Bass classes of modules.
The constructions of derived functors providing the triangulated
equivalence are based on a generalization of a technique developed
in our previous paper [45]. received 24.09.2018, accepted 30.04.2019 (77 pages)
download: manuscript (803K)
 Luyen, D.T.
Abstract: In this article, we study the multiplicity of weak solutions to the boundary value problem
\begin{eqnarray*}
G_\alpha u&=& g(x,y,u) + f(x,y,u) \ \mbox{ in }\ \ \Omega,\\
u&=&\ 0 \hskip 3cm \mbox{ on }\ \partial \Omega, \notag
\end{eqnarray*}
where $\Omega$ is a bounded domain with smooth boundary in $\mathbb{R}^N \ (N \ge 2), \alpha \in \mathbb{N}, g(x,y,\xi),$
$ f(x,y,\xi) $ are Carathéodory functions and $ G_\alpha $ is the Grushin operator. We use the lower bounds of eigenvalues and an abstract theory on signchanging solutions. received 01.04.2019, accepted 19.04.2019 (16 pages)
download: manuscript (370K)
 Alexandru V., Achimescu S. and Andronescu C.S.
Abstract: Let $(K,\cdot )$ be a local field. In this paper we define an invariant analogous to the discriminant over $K$ for certain transcendental elements over $K$. received 03.12.2018, accepted 28.03.2019 (8 pages)
download: manuscript (282K)
 Albrecht, Ulrich and McQuaig, Bradley
Abstract: This paper investigates the projective dimension of the maximal right ring of quotients $Q^r(R)$ of a right nonsingular ring $R$. Our discussion addresses the question under which conditions $p.d.(Q) \leq 1$ guarantees that the module $Q/R$ is a direct sum of countably generated modules extending Matlis' Theorem for integral domains to a noncommutative setting. received 11.12.2018, accepted 25.03.2019 (16 pages)
download: manuscript (355K)
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