University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
7
1
2019
06
01
On the Class of Subsets of Residuated lattice which induces a Congruence Relation
1
12
EN
H.
Harizavi
Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran
harizavi@scu.ac.ir
10.22124/jart.2019.11333.1119
In this manuscript, we study the class of special subsets connected with a subset in a residuated lattice and investigate some related properties. We describe the union of elements of this class. Using the intersection of all special subsets connected with a subset, we give a necessary and sufficient condition for a subset to be a filter. Finally, by defining some operations, we endow this class with a residuated lattice structure and prove that it is isomorphic to the set of all congruence classes with respect to a filter.
Residuated lattice,Filter,Complement-closed,Congruence Relation
https://jart.guilan.ac.ir/article_3687.html
https://jart.guilan.ac.ir/article_3687_5299c0b4ef0a8acd5f965ad25c45b012.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
7
1
2019
06
01
e-lifting modules relative to fully invariant submodules
13
24
EN
F.
Alizadeh
Department of Mathematics, Faculty of Basic Sciences, Babol University of Technology
Babol, Iran
fatemeh.alizadeh.ghadikolaei@gmail.com
M.
Hosseinpour
Department of Mathematics, Faculty of Mathematical Sciences,
University of Mazandaran, Babolsar, Iran
mehrab.hosseinpour@gmail.com
Z.
Kamali
Department of Mathematics, Faculty of Basic Sciences, Babol University of Technology
Babol, Iran
kamalih1357@gmail.com
10.22124/jart.2019.11972.1135
In this paper, we introduce the notion FI-e-lifting modules which is a proper generalization of lifting (e-lifting) modules.<br />Then we give some characterizations and properties of e-lifting and FI-e-lifting modules. We provide a decomposition of any e-lifting modules. It is shown that every finite direct sum of FI-e-lifting modules is FI-e-lifting
e-small submodules,e-lifting modules,FI-e-lifting modules
https://jart.guilan.ac.ir/article_3688.html
https://jart.guilan.ac.ir/article_3688_49b594f8898e605a0b32c9c9363b1c0a.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
7
1
2019
06
01
The inverse monoid associated to a group and the semidirect product of groups
25
34
EN
N.
Ghadbane
Laboratory of Pure and Applied Mathematics , Department of Mathematics, University of M'sila, B.P 166, Msila, Algeria
nacer.ghadbane@yahoo.com
10.22124/jart.2019.11348.1120
In this paper, we construct an inverse monoid $M\left( G\right) $ associated<br />to a given group $G$ by using the notion of the join of subgroups and then,<br />by applying the left action of monoid $M$ on a semigroup $S$, we form a<br />semigroup $S\omega M$ on the set $S\times M$. The finally result is to build<br />the semi direct product of groups associated to the group action on an<br />another group.
Semigroup,idempotents of semigroup,inverses of semigroup
https://jart.guilan.ac.ir/article_3689.html
https://jart.guilan.ac.ir/article_3689_23c7465e7ec64a0cf73dc61c9ecc1e2d.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
7
1
2019
06
01
The $ k $-${\rm \bf{ th}}$ spectral moment of signed complete graphs
35
44
EN
S.
Dalvandi
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
s.dalvandi@kiau.ac.ir
F.
Heydari
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
faride.heydari@gmail.com
M.
Maghasedi
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
maghasedi@kiau.ac.ir
10.22124/jart.2019.13670.1150
Let $\Gamma=(G,\sigma)$ be a signed graph, where $G$ is the underlying simple graph with at least one edge and $\sigma : E(G) \longrightarrow \lbrace -,+\rbrace$ is the sign function on the edges of $G$. In this paper, we study the $ k $-th spectral moment of $(K_n,\sigma)$, for a signature $\sigma$. Also, we obtain the number of negative cycles in a signed complete graph whose negative edges induce the disjoint union of two distinct complete bipartite graphs.
Signed graph,complete bipartite graph,negative cycle
https://jart.guilan.ac.ir/article_3690.html
https://jart.guilan.ac.ir/article_3690_d67598716ecc8ae5483f54f2bc56eeb6.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
7
1
2019
06
01
2-absorbing delta-primary elements in multiplicative lattices
45
64
EN
J. Y.
Nehete
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad.
jaya.nehete88@gmail.com
S. K.
Nimbhorkar
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad
sknimbhorkar@gmail.com
10.22124/jart.2019.11322.1118
In this paper, we define a 2-absorbing $\delta$-primary element and a weakly 2-absorbing $\delta$-primary element in a compactly generated multiplicative lattice $L$. We obtain some properties of these elements. We give a characterization for 2-absorbing $\delta$-primary elements. Also we define a $\delta$-triple-zero and a free $\delta$-triple-zero and prove some results on it.
Expansion function,2-absorbing $\delta$-primary element,weakly 2-absorbing $\delta$-primary element,$\delta$-triple-zero,free $\delta$-triple-zero
https://jart.guilan.ac.ir/article_3720.html
https://jart.guilan.ac.ir/article_3720_9e026b8035731c9bbb5e771f954a466f.pdf
University of Guilan
Journal of Algebra and Related Topics
2345-3931
2382-9877
7
1
2019
06
01
A new Gaussian Fibonacci matrices and its applications
65
72
EN
B.
Prasad
Kandi Raj College, Kandi, India
bandhu_iit@rediffmail.com
10.22124/jart.2019.12999.1144
In this paper, we introduced a new Gaussian Fibonacci matrix, $G^{n}$ whose elements are Gaussian Fibonacci numbers and we developed a new coding and decoding method followed from this Gaussian Fibonacci matrix, $G^{n}$. We established the relations between the code matrix elements, error detection and correction for this coding theory. Correction ability of this method is $93.33$\%.
Gaussian Fibonacci numbers,Fibonacci numbers,Golden mean
https://jart.guilan.ac.ir/article_3721.html
https://jart.guilan.ac.ir/article_3721_49da7f8b20ac8534782e530a53b0cea1.pdf