DOI: https://doi.org/10.14710/jfma.v5i1.11644

IDEMPOTENT MATRIX OVER SKEW GENERALIZED POWER SERIES RINGS

*Ahmad Faisol orcid  -  Universitas Lampung, Indonesia
Fitriani Fitriani orcid  -  Universitas Lampung, Indonesia

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Abstract

Let $R[[S,\leq,\omega]]$ be a skew generalized power series ring, with $R$ is a ring with an identity element, $(S,\leq)$ a strictly ordered monoid, and $\omega:S\rightarrow End(R)$ a monoid homomorphism. We define  the set of all matrices over $R[[S,\leq,\omega]]$, denoted by $M_{n}(R[[S,\leq,\omega]])$. With the addition and multiplication matrix operations, $M_{n}(R[[S,\leq,\omega]])$ becomes a ring. In this paper, we determine the sufficient conditions for $R$, $(S,\leq)$, and $\omega$, so the element of $M_{n}(R[[S,\leq,\omega]])$ is an idempotent matrix. 

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Keywords: idempotent matrix; matrices over a ring; strictly ordered monoid; monoid homomorphism; skew generalized power series ring
Funding: Research Institutions and Community Service of Universitas Lampung under contract No: 1648/UN 26.21/PN/2021

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Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : EN
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