@Article{Halicioglu2015,
author="Halicioglu, S.
and Calci, M. B.
and Harmanci, A.",
title="A class of J-quasipolar rings",
journal="Journal of Algebra and Related Topics",
year="2015",
volume="3",
number="2",
pages="1-15",
abstract="In this paper, we introduce a class of $J$-quasipolar rings. Let $R$ be a ring with identity. An element $a$ of a ring $R$ is called {\it weakly $J$-quasipolar} if there exists $p^2 = p\in comm^2(a)$ such that $a + p$ or $a-p$ are contained in $J(R)$ and the ring $R$ is called {\it weakly $J$-quasipolar} if every element of $R$ is weakly $J$-quasipolar. We give many characterizations and investigate general properties of weakly $J$-quasipolar rings. If $R$ is a weakly $J$-quasipolar ring, then we show that (1) $R/J(R)$ is weakly $J$-quasipolar, (2) $R/J(R)$ is commutative, (3) $R/J(R)$ is reduced. We use weakly $J$-quasipolar rings to obtain more results for $J$-quasipolar rings. We prove that the class of weakly $J$-quasipolar rings lies between the class of $J$-quasipolar rings and the class of quasipolar rings. Among others it is shown that a ring $R$ is abelian weakly $J$-quasipolar if and only if $R$ is uniquely clean.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_1537.html"
}
@Article{KrishnaKishore2015,
author="Krishna Kishore, M. Phani",
title="Omega-almost Boolean rings",
journal="Journal of Algebra and Related Topics",
year="2015",
volume="3",
number="2",
pages="17-25",
abstract="In this paper the concept of an $\Omega$- Almost Boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $\Omega$- Almost Boolean ring over a locally Boolean space.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_1538.html"
}
@Article{EbrahimiSarvandi2015,
author="Ebrahimi Sarvandi, Z.
and Ebrahimi Atani, S.",
title="The total graph of a commutative semiring with respect to proper ideals",
journal="Journal of Algebra and Related Topics",
year="2015",
volume="3",
number="2",
pages="27-41",
abstract="Let $I$ be a proper ideal of a commutative semiring $R$ and let $P(I)$ be the set of all elements of $R$ that are not prime to $I$. In this paper, we investigate the total graph of $R$ with respect to $I$, denoted by $T(\Gamma_{I} (R))$. It is the (undirected) graph with elements of $R$ as vertices, and for distinct $x, y \in R$, the vertices $x$ and $y$ are adjacent if and only if $x + y \in P(I)$. The properties and possible structures of the two (induced) subgraphs $P(\Gamma_{I} (R))$ and $\bar {P}(\Gamma_{I} (R))$ of $T(\Gamma_{I} (R))$, with vertices $P(I)$ and $R - P(I)$, respectively are studied.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_1539.html"
}
@Article{Beyranvand2015,
author="Beyranvand, R.
and Moradi, F.",
title="Small submodules with respect to an arbitrary submodule",
journal="Journal of Algebra and Related Topics",
year="2015",
volume="3",
number="2",
pages="43-51",
abstract="Let $R$ be an arbitrary ring and $T$ be a submodule of an $R$-module $M$. A submodule $N$ of $M$ is called $T$-small in $M$ provided for each submodule $X$ of $M$, $T\subseteq X+N$ implies that $T\subseteq X$. We study this mentioned notion which is a generalization of the small submodules and we obtain some related results.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_1540.html"
}
@Article{Yang2015,
author="Yang, S.
and Chu, L.
and Qian, Y.",
title="Castelnuovo-Mumford regularity of products of monomial ideals",
journal="Journal of Algebra and Related Topics",
year="2015",
volume="3",
number="2",
pages="53-59",
abstract="Let $R=k[x_1,x_2,\cdots, x_N]$ be a polynomial ring over a field $k$. We prove that for any positive integers $m, n$, $\text{reg}(I^mJ^nK)\leq m\text{reg}(I)+n\text{reg}(J)+\text{reg}(K)$ if $I, J, K\subseteq R$ are three monomial complete intersections ($I$, $J$, $K$ are not necessarily proper ideals of the polynomial ring $R$), and $I, J$ are of the form $(x_{i_1}^{a_1}, x_{i_2}^{a_2}, \cdots, x_{i_l}^{a_l})$.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_1541.html"
}
@Article{Polkouei2015,
author="Polkouei, M.
and Hashemi, M.",
title="nth-roots and n-centrality of finite 2-generator p-groups of nilpotency class 2",
journal="Journal of Algebra and Related Topics",
year="2015",
volume="3",
number="2",
pages="61-71",
abstract="Here we consider all finite non-abelian 2-generator $p$-groups ($p$ an odd prime) of nilpotency class two and study the probability of having $n^{th}$-roots of them. Also we find integers $n$ for which, these groups are $n$-central.",
issn="2345-3931",
doi="",
url="https://jart.guilan.ac.ir/article_1542.html"
}