Yazd University Algebraic Structures and Their Applications 2382-9761 2423-3447 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 2423-3447 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, India A. PARMAR Saurashtra University, Rajkot, India  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 2423-3447 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 2423-3447 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 2423-3447 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 2423-3447 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