eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2017-09-01
5
1
1
13
10.22044/jas.2017.994
994
MOST RESULTS ON A-IDEALS IN MV -MODULES
S. Saidi Goraghani
kouroshsaidi31@gmail.com
1
R. A. Borzooei
borzooei@sbu.ac.ir
2
Department of Mathematics, University of Farhangian, Tehran, Iran.
Department of Mathematics, University of Shahid Beheshti, Tehran, Iran.
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 $1leq jleq n$.
http://jas.shahroodut.ac.ir/article_994_dd6f0758634fc1dfcc2fb67c9d67677e.pdf
MV-algebra
MV-module
Prime A-ideal
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2017-09-01
5
1
15
25
10.22044/jas.2017.995
995
AN INDUCTIVE FUZZY DIMENSION
M. Abry
mabry@du.ac.ir
1
Jafar Zanjani
j_zanjani@std.du.ac.ir
2
School of Mathematics and Computer Science, University of Damghan, P.O. Box 3671641167, Damghan, Iran.
School of Mathematics and Computer science, University of Damghan, P.O.Box 3671641167, Damghan, Iran.
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.
http://jas.shahroodut.ac.ir/article_995_5557c9774af984cbc69e62c98e4c2f2a.pdf
Fuzzy topology
Intuitionistic fuzzy boundary
Fuzzy inductive dimension
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2017-09-01
5
1
27
51
10.22044/jas.2017.996
996
TABLE OF MARKS OF FINITE GROUPS
M. Ghorbani
mghorbani@srttu.edu
1
F. Abbasi
ghorbani30@gmail.com
2
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785{136, I. R. Iran
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785{136, I. R. Iran
Let G be a finite 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 fixed 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.
http://jas.shahroodut.ac.ir/article_996_a1fbc5e498c184e7f032d12626d80c2e.pdf
Frobenius group
table of marks
conjugacy class of subgroup
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2017-09-01
5
1
53
64
10.22044/jas.2017.997
997
GENERALIZED GORENSTEIN DIMENSION OVER GROUP RINGS
Abdolnaser Bahlekeh
n.bahlekeh@gmail.com
1
T. Kakaie
tkakaie@sci.ui.ac.ir
2
Department of Mathematics, Gonbad Kavous University, P.O. Box 4971799151, Gonbad Kavous, Iran.
Department of Mathematics, University of Isfahan, P.O. Box: 81746-73441, Isfa- han, Iran.
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.
http://jas.shahroodut.ac.ir/article_997_21bc08b517c81172cdbfcee37f64093c.pdf
Semi-dualizing bimodules
generalized Gorenstein dimension
group rings
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2017-09-01
5
1
65
72
10.22044/jas.2017.998
998
SOME REMARKS ON ALMOST UNISERIAL RINGS AND MODULES
H. R. Dorbidi
hr_dorbidi@ujiroft.ac.ir
1
Department of Mathematics, Faculty of Science, University of Jiroft, P.O. Box 78671-61167, Jiroft, Iran.
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.
http://jas.shahroodut.ac.ir/article_998_50b733a4cdef7a3d8368c4489791fda6.pdf
Almost uniserial rings
Almost uniserial modules
Socle of a module
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2017-09-01
5
1
73
84
10.22044/jas.2017.999
999
ON THE MAXIMAL SPECTRUM OF A MODULE
H. Ansari-Toroghy
ansari@guilan.ac.ir
1
S. Keivani
siamak.keyvani@gmail.com
2
Department of Pure Mathematics, Faculty of Mathematical Science, University of Guilan, P.O. Box 41335-19141, Rasht, Iran.
Department of Mathematics, Bandar Anzali Branch, Islamic Azad University, Ban- dar Anzali, Iran.
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.
http://jas.shahroodut.ac.ir/article_999_cfe480525b3eeb4d299ad10c3f1a4a16.pdf
Prime submodule
maximal submodule
Max-injective module
Max-strongly top module
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2017-09-01
5
1
85
90
10.22044/jas.2017.882
882
A NOTE ON THE COMMUTING GRAPHS OF A CONJUGACY CLASS IN SYMMETRIC GROUPS
Seyed H. Jafari
shjafari55@gmail.com
1
Department of Mathematics, Shahrood University of Technology, P.O. Box 3619995161-316, Shahrood, Iran.
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.
http://jas.shahroodut.ac.ir/article_882_47d09a8a2984aa2088d6a1c7f4a6b771.pdf
symmetric group
automorphim group
commuting graph