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2021β€’Asian-European Journal of MathematicsRequires access

The congruence π’΄βˆ— on quasi completely regular semirings

S. K. Maity, Rituparna Ghosh

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Abstract

A semiring [Formula: see text] is said to be a quasi-orthodox semiring if for any [Formula: see text], there exists some positive integer [Formula: see text] such that [Formula: see text]. In this paper, we investigate the congruence generated by [Formula: see text] on quasi completely regular semirings with and without the special conditions like being quasi-orthodox. We further establish that the interval which [Formula: see text] belongs to is [Formula: see text].

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What this paper is about

A semiring [Formula: see text] is said to be a quasi-orthodox semiring if for any [Formula: see text], there exists some positive integer [Formula: see text] such that [Formula: see text]. In this paper, we investigate the congruence generated by [Formula: see text] on quasi completely regular semirings with and without the special conditions like being quasi-orthodox. We further establish that the interval which [Formula: see text] belongs to is [Formula: see text].

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Available abstract

A semiring [Formula: see text] is said to be a quasi-orthodox semiring if for any [Formula: see text], there exists some positive integer [Formula: see text] such that [Formula: see text]. In this paper, we investigate the congruence generated by [Formula: see text] on quasi completely regular semirings with and without the special conditions like being quasi-orthodox. We further establish that the interval which [Formula: see text] belongs to is [Formula: see text].

Key concepts: Congruence (geometry), Semiring, Mathematics, Integer (computer science), Combinatorics, Interval (graph theory), Kleene algebra, Congruence relation

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