1999
DOI: 10.1007/bf02365069
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Semigroup rings with certain finiteness conditions

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1999
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“…Therefore, by Corollary 3.3 of [11], the semigroup S satisfies the minimal condition on left congruences. Let G be an arbitrary subgroup of S. Since the left ideal lattice of RG is embedded into the left ideal lattice of RS (see [12,Proposition 3.1]), the ring RG is left Artinian.…”
Section: Theorem 24 ([23 Theorem 3]) Let R Be a Ring And Let S Bementioning
confidence: 87%
“…Therefore, by Corollary 3.3 of [11], the semigroup S satisfies the minimal condition on left congruences. Let G be an arbitrary subgroup of S. Since the left ideal lattice of RG is embedded into the left ideal lattice of RS (see [12,Proposition 3.1]), the ring RG is left Artinian.…”
Section: Theorem 24 ([23 Theorem 3]) Let R Be a Ring And Let S Bementioning
confidence: 87%