Yazd University
Algebraic Structures and Their Applications
2382-9761
2
2
2015
11
01
Characterization and axiomatization of all semigroups whose square is group
1
8
EN
M.H.
Hooshmand
Shiraz Branch, Islamic Azad University
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 $S^2leq S$ (the square-group property) will be considered.
Ideal subgroup,grouplike,homogroup,class united grouplike,real grouplike
http://as.yazd.ac.ir/article_741.html
http://as.yazd.ac.ir/article_741_50a5e5f483c3aa4d91f526deacc2e032.pdf
Yazd University
Algebraic Structures and Their Applications
2382-9761
2
2
2015
11
01
When does the complement of the annihilating-ideal graph of a commutative ring admit a cut vertex?
9
22
EN
S.
VISWESWARAN
Saurashtra University, Rajkot
A.
PARMAR
Saurashtra University, Rajkot
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.
N-prime of $(0)$,B-prime of $(0)$,complement of the annihilating-ideal graph of a commutative ring,vertex cut and cut vertex of a connected graph
http://as.yazd.ac.ir/article_765.html
http://as.yazd.ac.ir/article_765_b8befa609c45c0b6b6a79bc456253b4a.pdf
Yazd University
Algebraic Structures and Their Applications
2382-9761
2
2
2015
11
01
Ultra and Involution Ideals in $BCK$-algebras
23
36
EN
Simin
Saidi Goraghani
Farhangian University
siminsaidi@yahoo.com
R. A.
Borzooei
Shahid Beheshti University
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.
$BCK$-algebra,(associative,commutative,positive implicative,implicative) ideal,ultra ideal,involution ideal
http://as.yazd.ac.ir/article_784.html
http://as.yazd.ac.ir/article_784_59ea8d93f1f07746b0ae002a32a6a389.pdf
Yazd University
Algebraic Structures and Their Applications
2382-9761
2
2
2015
11
01
The structure of a pair of nilpotent Lie algebras
37
47
EN
Homayoon
Arabyani
Islamic Azad University
arabyani_h@yahoo.com
Hadi Hosseini
Fadravi
Islamic Azad University
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.
Nilpotent Lie algebra,Pair of Lie algebras,Schur multiplier
http://as.yazd.ac.ir/article_785.html
http://as.yazd.ac.ir/article_785_f8abf078bb44933f3c1b0a1d39b66275.pdf
Yazd University
Algebraic Structures and Their Applications
2382-9761
2
2
2015
11
01
On the nil-clean matrix over a UFD
49
55
EN
Somayeh
Hadjirezaei
Vali-e-Asr University of Rafsanjan
s.hajirezaei@vru.ac.ir
Somayeh
Karimzadeh
Vali-e-Asr University of Rafsanjan
In this paper we characterize all $2times 2$ idempotent and nilpotent matrices over an integral domain and then we characterize all $2times 2$ strongly nil-clean matrices over a PID. Also, we determine when a $2times 2$ matrix over a UFD is nil-clean.
Rank of a matrix,Idempotent matrix,Nilpotent matrix,Nil-clean matrix,Strongly nil-clean matrix
http://as.yazd.ac.ir/article_803.html
http://as.yazd.ac.ir/article_803_7a98829c79d5ccc6521ac399e996e7bb.pdf
Yazd University
Algebraic Structures and Their Applications
2382-9761
2
2
2015
11
01
$z^circ$-filters and related ideals in $C(X)$
57
66
EN
Rostam
Mohamadian
Shahid Chamran University of Ahvaz
mohamadian_r@scu.ac.ir
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.
$z^circ$-filter,prime $z^circ$-filter,ci-free $z^circ$-filter,i-free $z^circ$-filter,$z^circ$-ultrafilter,i-compact
http://as.yazd.ac.ir/article_807.html
http://as.yazd.ac.ir/article_807_bb25ddc73dfd82df981f87a48bcc5e25.pdf