Journal•ISSN: 2345-3931

# Journal of Algebra and Related Topics

University of Guilan

About: Journal of Algebra and Related Topics is an academic journal. The journal publishes majorly in the area(s): Commutative ring & Ideal (ring theory). It has an ISSN identifier of 2345-3931. Over the lifetime, 86 publications have been published receiving 137 citations.

##### Papers

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TL;DR: In this article, a new algebraic structure, called a UP-algebra (UP means the University of Phayao) and a concept of UP-ideals, UP-subalgebras, congruences and UP-homomorphisms were introduced.

Abstract: In this paper, we introduce a new algebraic structure, called a UP-algebra (UP means the University of Phayao) and a concept of UP-ideals, UP-subalgebras, congruences and UP-homomorphisms in UP-algebras, and investigated some related properties of them. We also describe connections between UP-ideals, UP-subalgebras, congruences and UP-homomorphisms, and show that the notion of UP-algebras is a generalization of KU-algebras.

64 citations

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TL;DR: In this paper, a generalization of the small submodules, called small sub-modules, is introduced, where the sub-module is called small in a ring and the ring is an arbitrary ring.

Abstract: Let $R$ be an arbitrary ring and $T$ be a submodule of an $R$-module $M$. A submodule $N$ of $M$ is called $T$-small in $M$ provided for each submodule $X$ of $M$, $Tsubseteq X+N$ implies that $Tsubseteq X$. We study this mentioned notion which is a generalization of the small submodules and we obtain some related results.

8 citations

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TL;DR: The relations between $mathcal{N}$-fuzzy UP-subalgebras and its level subsets are discussed and their generalizations and characteristic are considered.

Abstract: In this paper, $mathcal{N}$-fuzzy UP-subalgebras (resp., $mathcal{N}$-fuzzy UP-filters, $mathcal{N}$-fuzzy UP-ideals and $mathcal{N}$-fuzzy strongly UP-ideals) of UP-algebras are introduced and considered their generalizations and characteristic $mathcal{N}$-fuzzy sets of UP-subalgebras (resp., UP-filters, UP-ideals and strongly UP-ideals).Further, we discuss the relations between $mathcal{N}$-fuzzy UP-subalgebras (resp., $mathcal{N}$-fuzzy UP-filters, $mathcal{N}$-fuzzy UP-ideals and $mathcal{N}$-fuzzy strongly UP-ideals) and its level subsets.

8 citations

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TL;DR: In this paper, the authors introduce the concept of the Zariski socles of submodules of sub-modules of $M$ and investigate their properties with Noetherian second spectrum.

Abstract: Let $R$ be a commutative ring and let $M$ be an $R$-module. In this article, we introduce the concept of the Zariski socles of submodules of $M$ and investigate their properties. Also we study modules with Noetherian second spectrum and obtain some related results.

8 citations

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TL;DR: A new Gaussian fibonacci matrix is introduced whose elements are Gaussian Fibonacci numbers and a new coding and decoding method is developed that established the relations between the code matrix elements, error detection and correction for this coding theory.

Abstract: 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 $93.33$%.

5 citations