Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
5
1
2017
09
01
MOST RESULTS ON A-IDEALS IN MV -MODULES
1
13
EN
S.
Saidi Goraghani
Department of Mathematics, University of Farhangian, Tehran, Iran.
kouroshsaidi31@gmail.com
R. A.
Borzooei
Department of Mathematics, University of Shahid Beheshti, Tehran, Iran.
borzooei@sbu.ac.ir
10.22044/jas.2017.994
In the present paper, by considering the notion of MV-modules which is the structure that naturally correspond to lu-modules over lu-rings, we prove some results on prime A-ideals and state some conditions to obtain a prime A-ideal in MV-modules. Also, we state some conditions that an A-ideal is not prime and investigate conditions that $Ksubseteq bigcup _{i=1}^{n}K_{i}$ implies $Ksubseteq K_{j}$, where $K,K_{1},cdots ,K_{n}$ are A-ideals of A-module M and $1leq jleq n$.
MV-algebra,MV-module,Prime A-ideal
http://jas.shahroodut.ac.ir/article_994.html
http://jas.shahroodut.ac.ir/article_994_dd6f0758634fc1dfcc2fb67c9d67677e.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
5
1
2017
09
01
AN INDUCTIVE FUZZY DIMENSION
15
25
EN
M.
Abry
School of Mathematics and Computer Science, University of Damghan, P.O. Box
3671641167, Damghan, Iran.
mabry@du.ac.ir
Jafar
Zanjani
School of Mathematics and Computer science, University of Damghan, P.O.Box 3671641167, Damghan, Iran.
j_zanjani@std.du.ac.ir
10.22044/jas.2017.995
Using a system of axioms among with a modified definition of boundary on the basis of the intuitionistic fuzzy sets, we formulate an inductive structure for the dimension of fuzzy spaces which has been defined by Coker. This new definition of boundary allows to characterize an intuitionistic fuzzy clopen set as a set with zero boundary. Also, some critical properties and applications are established.
Fuzzy topology,Intuitionistic fuzzy boundary,Fuzzy inductive dimension
http://jas.shahroodut.ac.ir/article_995.html
http://jas.shahroodut.ac.ir/article_995_5557c9774af984cbc69e62c98e4c2f2a.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
5
1
2017
09
01
TABLE OF MARKS OF FINITE GROUPS
27
51
EN
M.
Ghorbani
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training
University, Tehran, 16785{136, I. R. Iran
mghorbani@srttu.edu
F.
Abbasi
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training
University, Tehran, 16785{136, I. R. Iran
ghorbani30@gmail.com
10.22044/jas.2017.996
Let G be a nite group and C(G) be the family of representative conjugacy classes of subgroups of G. The matrix whose H;K-entry is the number of xed points of the set G=K under the action of H is called the table of marks of G where H;K run through all elements in C(G). In this paper, we compute the table of marks and the markaracter table of groups of order pqr where p, q, r are prime numbers.
Frobenius group,table of marks,conjugacy class of subgroup
http://jas.shahroodut.ac.ir/article_996.html
http://jas.shahroodut.ac.ir/article_996_a1fbc5e498c184e7f032d12626d80c2e.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
5
1
2017
09
01
GENERALIZED GORENSTEIN DIMENSION OVER GROUP RINGS
53
64
EN
Abdolnaser
Bahlekeh
Department of Mathematics, Gonbad Kavous University, P.O. Box 4971799151,
Gonbad Kavous, Iran.
n.bahlekeh@gmail.com
T.
Kakaie
Department of Mathematics, University of Isfahan, P.O. Box: 81746-73441, Isfa-
han, Iran.
tkakaie@sci.ui.ac.ir
10.22044/jas.2017.997
Let $(R, m)$ be a commutative noetherian local ring and let $Gamma$ be a finite group. It is proved that if $R$ admits a dualizing module, then the group ring $Rga$ has a dualizing bimodule as well. Moreover, it is shown that a finitely generated $Rga$-module $M$ has generalized Gorenstein dimension zero if and only if it has generalized Gorenstein dimension zero as an $R$-module.
Semi-dualizing bimodules,generalized Gorenstein dimension,group rings
http://jas.shahroodut.ac.ir/article_997.html
http://jas.shahroodut.ac.ir/article_997_21bc08b517c81172cdbfcee37f64093c.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
5
1
2017
09
01
SOME REMARKS ON ALMOST UNISERIAL RINGS AND MODULES
65
72
EN
H. R.
Dorbidi
Department of Mathematics, Faculty of Science, University of Jiroft, P.O. Box
78671-61167, Jiroft, Iran.
hr_dorbidi@ujiroft.ac.ir
10.22044/jas.2017.998
In this paper we study almost uniserial rings and modules. An Râˆ’module M is called almost uniserial if any two nonisomorphic submodules are linearly ordered by inclusion. A ring R is an almost left uniserial ring if R_R is almost uniserial. We give some necessary and sufficient condition for an Artinian ring to be almost left uniserial.
Almost uniserial rings,Almost uniserial modules,Socle of a module
http://jas.shahroodut.ac.ir/article_998.html
http://jas.shahroodut.ac.ir/article_998_50b733a4cdef7a3d8368c4489791fda6.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
5
1
2017
09
01
ON THE MAXIMAL SPECTRUM OF A MODULE
73
84
EN
H.
Ansari-Toroghy
Department of Pure Mathematics, Faculty of Mathematical Science, University of
Guilan, P.O. Box 41335-19141, Rasht, Iran.
ansari@guilan.ac.ir
S.
Keivani
Department of Mathematics, Bandar Anzali Branch, Islamic Azad University, Ban-
dar Anzali, Iran.
siamak.keyvani@gmail.com
10.22044/jas.2017.999
Let $R$ be a commutative ring with identity. The purpose of this paper is to introduce and study two classes of modules over $R$, called $mbox{Max}$-injective and $mbox{Max}$-strongly top modules and explore some of their basic properties. Our concern is to extend some properties of $X$-injective and strongly top modules to these classes of modules and obtain some related results.
Prime submodule,maximal submodule,Max-injective module,Max-strongly top module
http://jas.shahroodut.ac.ir/article_999.html
http://jas.shahroodut.ac.ir/article_999_cfe480525b3eeb4d299ad10c3f1a4a16.pdf
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
5
1
2017
09
01
A NOTE ON THE COMMUTING GRAPHS OF A CONJUGACY CLASS IN SYMMETRIC GROUPS
85
90
EN
Seyed H.
Jafari
Department of Mathematics, Shahrood University of Technology, P.O. Box
3619995161-316, Shahrood, Iran.
shjafari55@gmail.com
10.22044/jas.2017.882
The commuting graph of a group is a graph with vertexes set of a subset of a group and two element are adjacent if they commute. The aim of this paper is to obtain the automorphism group of the commuting graph of a conjugacy class in the symmetric groups. The clique number, coloring number, independent number, and diameter of these graphs are also computed.
symmetric group,automorphim group,commuting graph
http://jas.shahroodut.ac.ir/article_882.html
http://jas.shahroodut.ac.ir/article_882_47d09a8a2984aa2088d6a1c7f4a6b771.pdf