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2019•Publicationes Mathematicae DebrecenRequires access

On the additive and multiplicative structures of the exceptional units in finite commutative rings

Su Hu, Min Sha

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Abstract

Let R be a commutative ring with identity.A unit u of R is called exceptional if 1u is also a unit.When R is a finite commutative ring, we determine the additive and multiplicative structures of its exceptional units; and then as an application we find a necessary and sufficient condition under which R is generated by its exceptional units.

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What this paper is about

Let R be a commutative ring with identity.A unit u of R is called exceptional if 1u is also a unit.When R is a finite commutative ring, we determine the additive and multiplicative structures of its exceptional units; and then as an application we find a necessary and sufficient condition under which R is generated by its exceptional units.

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OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Let R be a commutative ring with identity.A unit u of R is called exceptional if 1u is also a unit.When R is a finite commutative ring, we determine the additive and multiplicative structures of its exceptional units; and then as an application we find a necessary and sufficient condition under which R is generated by its exceptional units.

Key concepts: Multiplicative function, Commutative ring, Mathematics, Unit (ring theory), Commutative property, Ring (chemistry), Pure mathematics, Identity (music)

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