Characterization and axiomatization of all semigroups whose square is group
M.H.
Hooshmand
Shiraz Branch, Islamic Azad University
author
text
article
2015
eng
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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
2
v.
2
no.
2015
1
8
http://as.yazd.ac.ir/article_741_50a5e5f483c3aa4d91f526deacc2e032.pdf
When does the complement of the annihilating-ideal graph of a commutative ring admit a cut vertex?
S.
VISWESWARAN
Saurashtra University, Rajkot, India
author
A.
PARMAR
Saurashtra University, Rajkot, India
author
text
article
2015
eng
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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
2
v.
2
no.
2015
9
22
http://as.yazd.ac.ir/article_765_b8befa609c45c0b6b6a79bc456253b4a.pdf
Ultra and Involution Ideals in $BCK$-algebras
Simin
Saidi Goraghani
Farhangian University
author
R. A.
Borzooei
Shahid Beheshti University
author
text
article
2015
eng
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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
2
v.
2
no.
2015
23
36
http://as.yazd.ac.ir/article_784_59ea8d93f1f07746b0ae002a32a6a389.pdf
The structure of a pair of nilpotent Lie algebras
Homayoon
Arabyani
Islamic Azad University
author
Hadi Hosseini
Fadravi
Islamic Azad University
author
text
article
2015
eng
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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
2
v.
2
no.
2015
37
47
http://as.yazd.ac.ir/article_785_f8abf078bb44933f3c1b0a1d39b66275.pdf
On the nil-clean matrix over a UFD
Somayeh
Hadjirezaei
Vali-e-Asr University of Rafsanjan
author
Somayeh
Karimzadeh
Vali-e-Asr University of Rafsanjan
author
text
article
2015
eng
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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
2
v.
2
no.
2015
49
55
http://as.yazd.ac.ir/article_803_7a98829c79d5ccc6521ac399e996e7bb.pdf
$z^\circ$-filters and related ideals in $C(X)$
Rostam
Mohamadian
Shahid Chamran University of Ahvaz
author
text
article
2015
eng
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.
Algebraic Structures and Their Applications
Yazd University
2382-9761
2
v.
2
no.
2015
57
66
http://as.yazd.ac.ir/article_807_bb25ddc73dfd82df981f87a48bcc5e25.pdf