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2022•AIP conference proceedingsRequires access

Antisimple Γ – Semirings and conditions on a Γ – Semiring with strong identity

Tilak Raj Sharma, Anuj Sharma, Ritu Sharma

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Abstract

In this paper, we introduce the notion of a antisimple Γ– semiring and Dale norm. If R is a Γ– semiring on which dale norm is defined then R is Γ– entire. Further let R be a commutative antisimple Γ– semiring and f: R → ℕ be a Dale norm then R is isomorphic to either ℕ or (ℕ ∪ (-∞) or a division Γ– semiring. Finally, we study some conditions of a Γ– semiring with strong identity regarding centreless, commutative additively idempotent, derivation of R and multiplicatively strong Γ–idempotent.

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What this paper is about

In this paper, we introduce the notion of a antisimple Γ– semiring and Dale norm. If R is a Γ– semiring on which dale norm is defined then R is Γ– entire. Further let R be a commutative antisimple Γ– semiring and f: R → ℕ be a Dale norm then R is isomorphic to either ℕ or (ℕ ∪ (-∞) or a division Γ– semiring. Finally, we study some conditions of a Γ– semiring with strong identity regarding centreless, commutative additively idempotent, derivation of R and multiplicatively strong Γ–idempotent.

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Available abstract

In this paper, we introduce the notion of a antisimple Γ– semiring and Dale norm. If R is a Γ– semiring on which dale norm is defined then R is Γ– entire. Further let R be a commutative antisimple Γ– semiring and f: R → ℕ be a Dale norm then R is isomorphic to either ℕ or (ℕ ∪ (-∞) or a division Γ– semiring. Finally, we study some conditions of a Γ– semiring with strong identity regarding centreless, commutative additively idempotent, derivation of R and multiplicatively strong Γ–idempotent.

Key concepts: Semiring, Idempotence, Mathematics, Norm (philosophy), Commutative property, Identity (music), Discrete mathematics, Combinatorics

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