Unique factorization properties in commutative monoid rings with zero divisors

Autor:	Christopher Mooney, Rhys D. Roberts, J. R. Juett
Rok vydání:	2021
Předmět:	Principal ideal ring Monoid Ring (mathematics) Pure mathematics Algebra and Number Theory Mathematics::Commutative Algebra Semigroup 010102 general mathematics Unique factorization domain 0102 computer and information sciences Commutative ring 01 natural sciences 010201 computation theory & mathematics Ideal (ring theory) 0101 mathematics Zero divisor Mathematics
Zdroj:	Semigroup Forum. 102:674-696
ISSN:	1432-2137 0037-1912
DOI:	10.1007/s00233-020-10154-x
Popis:	Several different versions of “factoriality” have been defined for commutative rings with zero divisors. We apply semigroup theory to study these notions in the context of a commutative monoid ring R[S], determining necessary and sufficient conditions for R[S] to be various kinds of “unique factorization rings.” Our work generalizes Anderson et al.’s results about “unique factorization” in R[X], Gilmer and Parker’s characterization of factorial monoid domains, and Hardy and Shores’s classification of when R[S] is a principal ideal ring (for S cancellative). Along the way, we determine when R[S] is “restricted cancellative” or satisfies various “(restricted) ideal cancellation laws.”
Databáze:	OpenAIRE
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