eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2013-09-15
1
1
1
9
10.22044/jas.2013.169
169
UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES
Moharram Aghapournahr
m.aghapour@gmail.com
1
Department of Mathematics, Faculty of Science, Arak University, Arak, 38156-8-8349, Iran.
Let $R$ be a commutative Noetherian ring with non-zero identity and $a$ an ideal of $R$. Let $M$ be a finite $R$--module<br />of finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $H^{i}_{a}(M,N)$ in certain Serre subcategories of the category of modules from upper bounds. We define and study the properties of a generalization of cohomological dimension of generalized local cohomology modules. Let $mathcal S$ be a Serre subcategory of the category of $R$--modules and $n > pd M$ be an integer such that $H^{i}_{a}(M,N)$ belongs to $mathcal S$ for all $i> n$. Then, for any ideal $bsupseteq a$, it is also shown that the module $H^{n}_{a}(M,N)/{b}H^{n}_{a}(M,N)$ belongs to $mathcal S$.<br /><br />
http://jas.shahroodut.ac.ir/article_169_c37d47751d382a040ab25cdfc4d74ec6.pdf
Generalized local cohomology module
Serre subcategory
cohomological dimension
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2013-09-15
1
1
11
31
10.22044/jas.2013.167
167
f-DERIVATIONS AND (f; g)-DERIVATIONS OF MV -ALGEBRAS
L. Kamali Ardakani
sdeh46@yahoo.com
1
Bijan Davvaz
davvaz@yazd.ac.ir
2
Department of Mathematics, Yazd University, Yazd, Iran.
Department of Mathematics, Yazd University, Yazd, Iran.
Recently, the algebraic theory of MV -algebras is intensively studied. <br />In this paper, we extend the concept of derivation of $MV$-algebras and we give some<br />illustrative examples. Moreover, as a generalization of derivations of $MV$ -algebras<br />we introduce the notion of $f$-derivations and $(f; g)$-derivations of $MV$-algebras.<br />Also, we investigate some properties of them.
http://jas.shahroodut.ac.ir/article_167_3a68dccc76e6f69f9a0255ccc7a9453a.pdf
MV -algebra
Lattice
BCIBCK-algebra
derivation
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2013-09-15
1
1
33
43
10.22044/jas.2013.166
166
NETS AND SEPARATED S-POSETS
Mahdieh Haddadi
haddadi_1360@yahoo.com
1
Department of Mathematics, Faculty of Mathematics, Statistics and computer science, Semnan University, Semnan, Iran.
Nets, useful topological tools, used to generalize certain concepts that may only be general enough in the context of metric<br />spaces. In this work we introduce this concept in an $S$-poset, a poset with an action of a posemigroup $S$ on it which<br />is a very useful structure in computer sciences and interesting for mathematicians, and give the the concept of $S$-net. Using $S$-nets and its convergency we also give some characterizations of separated $S$-posets. Also, introducing the net-closure operators, we investigate the counterparts of topological separation axioms on $S$-posets and study their relation to separated $S$-posets.
http://jas.shahroodut.ac.ir/article_166_38e125e00d02238374d1cc0c2152786e.pdf
$S$-poset
Separated $S$-poset
Separation axioms
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2013-09-15
1
1
45
52
10.22044/jas.2013.165
165
SOLVABILITY OF FREE PRODUCTS, CAYLEY GRAPHS AND COMPLEXES
Hanieh Mirebrahimi
h_mirebrahimi@um.ac.ir
1
Fatemeh Ghanei
fatemeh.ghanei91@gmail.com
2
Department of pure Mathematics, Ferdowsi University of Mashhad, P.O.Box 1159-91775 Mashhad, Iran
Department of pure Mathematics, Ferdowsi University of Mashhad, P.O.Box 1159-91775 Mashhad, Iran
In this paper, we verify the solvability of free product of finite cyclic groups with topological methods. We use Cayley graphs and Everitt methods to construct suitable 2-complexes corresponding to the presentations of groups and their commutator subgroups. In particular, using these methods, we prove that the commutator subgroup of ${Z}_{m}*{Z}_{n}$ is free of rank $(m-1)(n-1)$ for all $m,ngeq2$
http://jas.shahroodut.ac.ir/article_165_76e847bc1b83709351833bc141c00f5a.pdf
simplicial complex
fundamental group
covering space
Caley graph
solvable group
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2013-09-15
1
1
53
65
10.22044/jas.2013.164
164
ON SELBERG-TYPE SQUARE MATRICES INTEGRALS
Mohammad Arashi
m_arashi_stat@yahoo.com
1
Department of Statistics
School of Mathematics,
Shahrood University of Technology,
Shahrood, Iran.
In this paper we consider Selberg-type square matrices integrals with focus on Kummer-beta types I & II integrals. For generality of the results for real normed division algebras, the generalized matrix variate Kummer-beta types I & II are defined under the abstract algebra. Then Selberg-type integrals are calculated under<br />orthogonal transformations.
http://jas.shahroodut.ac.ir/article_164_0aa20d6e72bc0fdaf5b8905e0d0e5859.pdf
Selberg-Type integrals
Real normed division algebras
Kummer-beta distribution
Random matrix
eng
Shahrood University of Technology
Journal of Algebraic Systems
2345-5128
2345-511X
2013-09-15
1
1
67
77
10.22044/jas.2013.168
168
GENERALIZATIONS OF δ-LIFTING MODULES
Yahya Talebi
talebi@umz.ac.ir
1
Mehrab Hosseinpour
m.hpour@umz.ac.ir
2
Department of Mathematics, Faculty of Mathematical Sciences University of Mazandaran, Babolsar, Iran
Department of Mathematics, Faculty of Mathematical Sciences University of Mazandaran, Babolsar, Iran
In this paper we introduce the notions of $G_{1}^{*}L$-module and $G_{2}^{*}L$-module which are two proper generalizations of $delta$-lifting modules. We give some characterizations and properties of these modules. We show that a<br />$G_{2}^{*}L$-module decomposes into a semisimple submodule $M_{1}$ and a submodule $M_{2}$ of $M$ such that every non-zero submodule of $M_{2}$ contains a non-zero $delta$-cosingular submodule.
http://jas.shahroodut.ac.ir/article_168_779f9060623194a54be4107cc9186779.pdf
δ-cosingular
non-δ-cosingular
G∗L-module