فهرست مطالب

Algebra and Related Topic - Volume:7 Issue:1, 2019
  • Volume:7 Issue:1, 2019
  • تاریخ انتشار: 1398/03/11
  • تعداد عناوین: 6
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  • H. Harizavi * Pages 1-12
    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.
    Keywords: Residuated lattice, Filter, Complement-closed, Congruence Relation
  • F. Alizadeh, M. Hosseinpour *, Z. Kamali Pages 13-24
    In this paper, we introduce the notion FI-e-lifting modules which is a proper generalization of lifting (e-lifting) modules.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
    Keywords: e-small submodules, e-lifting modules, FI-e-lifting modules
  • N. Ghadbane * Pages 25-34
    In this paper, we construct an inverse monoid $Mleft( Gright) $ associatedto a given group $G$ by using the notion of the join of subgroups and then,by applying the left action of monoid $M$ on a semigroup $S$, we form asemigroup $Somega M$ on the set $Stimes M$. The finally result is to buildthe semi direct product of groups associated to the group action on ananother group.
    Keywords: Semigroup, idempotents of semigroup, inverses of semigroup
  • S. Dalvandi, F. Heydari *, M. Maghasedi Pages 35-44
    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.
    Keywords: Signed graph, complete bipartite graph, negative cycle
  • J. Y. Nehete *, S. K. Nimbhorkar Pages 45-64
    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.
    Keywords: Expansion function, 2-absorbing $delta$-primary element, weakly 2-absorbing $delta$-primary element, $delta$-triple-zero, free $delta$-triple-zero
  • B. Prasad * Pages 65-72
    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 $93.33$%.
    Keywords: Gaussian Fibonacci numbers, Fibonacci numbers, Golden mean