@Article{Hooshmand2015,
author="Hooshmand, M.H.",
title="Characterization and axiomatization of all semigroups whose square is group",
journal="Algebraic Structures and Their Applications",
year="2015",
volume="2",
number="2",
pages="1-8",
abstract="In this paper we give a characterization for all semigroups whose square is a group. Moreover, we axiomatize such semigroups and study some relations between the class of these semigroups and Grouplikes,introduced by the author. Also, we observe that this paper characterizes and axiomatizes a class of Homogroups (semigroups containing an ideal subgroup). Finally, several equivalent conditions for a semigroup $S$ with $S^2\leq S$ (the square-group property) will be considered.",
issn="2382-9761",
doi="",
url="http://as.yazd.ac.ir/article_741.html"
}
@Article{VISWESWARAN2015,
author="VISWESWARAN, S.
and PARMAR, A.",
title="When does the complement of the annihilating-ideal graph of a commutative ring admit a cut vertex?",
journal="Algebraic Structures and Their Applications",
year="2015",
volume="2",
number="2",
pages="9-22",
abstract=" The rings considered in this article are commutative with identity which admit at least two nonzero annihilating ideals. Let $R$ be a ring. Let $\mathbb{A}(R)$ denote the set of all annihilating ideals of $R$ and let $\mathbb{A}(R)^{*} = \mathbb{A}(R)\backslash \{(0)\}$. The annihilating-ideal graph of $R$, denoted by $\mathbb{AG}(R)$ is an undirected simple graph whose vertex set is $\mathbb{A}(R)^{*}$ and distinct vertices $I, J$ are joined by an edge in this graph if and only if $IJ = (0)$. The aim of this article is to classify rings $R$ such that $(\mathbb{AG}(R))^{c}$ ( that is, the complement of $\mathbb{AG}(R)$) is connected and admits a cut vertex.",
issn="2382-9761",
doi="",
url="http://as.yazd.ac.ir/article_765.html"
}
@Article{SaidiGoraghani2015,
author="Saidi Goraghani, Simin
and Borzooei, R. A.",
title="Ultra and Involution Ideals in $BCK$-algebras",
journal="Algebraic Structures and Their Applications",
year="2015",
volume="2",
number="2",
pages="23-36",
abstract="In this paper, we define the notions of ultra and involution ideals in $BCK$-algebras. Then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. Specially, we show that in a bounded implicative $BCK$-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower $BCK$-semilattice, the notions of prime ideals and ultra ideals are coincide.",
issn="2382-9761",
doi="",
url="http://as.yazd.ac.ir/article_784.html"
}
@Article{Arabyani2015,
author="Arabyani, Homayoon
and Fadravi, Hadi Hosseini",
title="The structure of a pair of nilpotent Lie algebras",
journal="Algebraic Structures and Their Applications",
year="2015",
volume="2",
number="2",
pages="37-47",
abstract="Assume that $(N,L)$, is a pair of finite dimensional nilpotent Lie algebras, in which $L$ is non-abelian and $N$ is an ideal in $L$ and also $\mathcal{M}(N,L)$ is the Schur multiplier of the pair $(N,L)$. Motivated by characterization of the pairs $(N,L)$ of finite dimensional nilpotent Lie algebras by their Schur multipliers (Arabyani, et al. 2014) we prove some properties of a pair of nilpotent Lie algebras and generalize results for a pair of non-abelian nilpotent Lie algebras.",
issn="2382-9761",
doi="",
url="http://as.yazd.ac.ir/article_785.html"
}
@Article{Hadjirezaei2015,
author="Hadjirezaei, Somayeh
and Karimzadeh, Somayeh",
title="On the nil-clean matrix over a UFD",
journal="Algebraic Structures and Their Applications",
year="2015",
volume="2",
number="2",
pages="49-55",
abstract=" In this paper we characterize all $2\times 2$ idempotent and nilpotent matrices over an integral domain and then we characterize all $2\times 2$ strongly nil-clean matrices over a PID. Also, we determine when a $2\times 2$ matrix over a UFD is nil-clean.",
issn="2382-9761",
doi="",
url="http://as.yazd.ac.ir/article_803.html"
}
@Article{Mohamadian2015,
author="Mohamadian, Rostam",
title="$z^\circ$-filters and related ideals in $C(X)$",
journal="Algebraic Structures and Their Applications",
year="2015",
volume="2",
number="2",
pages="57-66",
abstract="In this article we introduce the concept of $z^\circ$-filter on a topological space $X$. We study and investigate the behavior of $z^\circ$-filters and compare them with corresponding ideals, namely, $z^\circ$-ideals of $C(X)$, the ring of real-valued continuous functions on a completely regular Hausdorff space $X$. It is observed that $X$ is a compact space if and only if every $z^\circ$-filter is ci-fixed. Finally, by using $z^\circ$-ultrafilters, we prove that any arbitrary product of i-compact spaces is i-compact.",
issn="2382-9761",
doi="",
url="http://as.yazd.ac.ir/article_807.html"
}