MATRIX MAPS OVER SEMINEARRINGS

S. P. Kuncham; S. Tapatee; S. Rajani; B. S. Kedukodi; P. K. Harikrishnan

MATRIX MAPS OVER SEMINEARRINGS

S. P. Kuncham
, S. Tapatee^*
, S. Rajani
, B. S. Kedukodi
, P. K. Harikrishnan^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this paper, we introduce the notion of a matrix seminearring (abbr. M_n(S)) over an arbitrary seminearring S. A (right) seminearring is a generalization of a semiring and a nearring, wherein (S, +) and (S, ·) are semigroups; with only one distributive law is assumed. We prove various properties of matrix maps over a seminearring and obtain a one-one correspondence between the ideals of a seminearring and that of full ideals of matrix seminearring. Furthermore, we introduce prime ideal in matrix sem-inearring and prove that the ideal P^∗, induced by a prime ideal P in S is prime in M_n(S).

Original language	English
Pages (from-to)	123-134
Number of pages	12
Journal	Global and Stochastic Analysis
Volume	10
Issue number	2
Publication status	Published - 12-2023

All Science Journal Classification (ASJC) codes

Statistics and Probability
Discrete Mathematics and Combinatorics

Cite this

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title = "MATRIX MAPS OVER SEMINEARRINGS",

abstract = "In this paper, we introduce the notion of a matrix seminearring (abbr. Mn(S)) over an arbitrary seminearring S. A (right) seminearring is a generalization of a semiring and a nearring, wherein (S, +) and (S, ·) are semigroups; with only one distributive law is assumed. We prove various properties of matrix maps over a seminearring and obtain a one-one correspondence between the ideals of a seminearring and that of full ideals of matrix seminearring. Furthermore, we introduce prime ideal in matrix sem-inearring and prove that the ideal P∗, induced by a prime ideal P in S is prime in Mn(S).",

author = "Kuncham, \{S. P.\} and S. Tapatee and S. Rajani and Kedukodi, \{B. S.\} and Harikrishnan, \{P. K.\}",

year = "2023",

month = dec,

language = "English",

volume = "10",

pages = "123--134",

journal = "Global and Stochastic Analysis",

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T1 - MATRIX MAPS OVER SEMINEARRINGS

AU - Kuncham, S. P.

AU - Tapatee, S.

AU - Rajani, S.

AU - Kedukodi, B. S.

AU - Harikrishnan, P. K.

PY - 2023/12

Y1 - 2023/12

N2 - In this paper, we introduce the notion of a matrix seminearring (abbr. Mn(S)) over an arbitrary seminearring S. A (right) seminearring is a generalization of a semiring and a nearring, wherein (S, +) and (S, ·) are semigroups; with only one distributive law is assumed. We prove various properties of matrix maps over a seminearring and obtain a one-one correspondence between the ideals of a seminearring and that of full ideals of matrix seminearring. Furthermore, we introduce prime ideal in matrix sem-inearring and prove that the ideal P∗, induced by a prime ideal P in S is prime in Mn(S).

AB - In this paper, we introduce the notion of a matrix seminearring (abbr. Mn(S)) over an arbitrary seminearring S. A (right) seminearring is a generalization of a semiring and a nearring, wherein (S, +) and (S, ·) are semigroups; with only one distributive law is assumed. We prove various properties of matrix maps over a seminearring and obtain a one-one correspondence between the ideals of a seminearring and that of full ideals of matrix seminearring. Furthermore, we introduce prime ideal in matrix sem-inearring and prove that the ideal P∗, induced by a prime ideal P in S is prime in Mn(S).

UR - https://www.scopus.com/pages/publications/85168969904

UR - https://www.scopus.com/pages/publications/85168969904#tab=citedBy

M3 - Article

AN - SCOPUS:85168969904

SN - 2248-9444

VL - 10

SP - 123

EP - 134

JO - Global and Stochastic Analysis

JF - Global and Stochastic Analysis

IS - 2

ER -

MATRIX MAPS OVER SEMINEARRINGS

Abstract

All Science Journal Classification (ASJC) codes

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