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2004•Unpublished venueRequires access

GPP-rings of generalized power series

Yang Xiaoyan

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Abstract

Let be a commutative ring and a strictly totally ordered monoid.In this paper we prove that the ring [[ ]] of generalized power series is a strongly ring if and only if is a strongly ring and every -indexed subset of (the set of all idempotents of )has a least upper bound in ,and if also satisfied the condition that for any .then the ring [[ ]] is weakly ring if and only if is weakly ring.

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What this paper is about

Let be a commutative ring and a strictly totally ordered monoid.In this paper we prove that the ring [[ ]] of generalized power series is a strongly ring if and only if is a strongly ring and every -indexed subset of (the set of all idempotents of )has a least upper bound in ,and if also satisfied the condition that for any .then the ring [[ ]] is weakly ring if and only if is weakly ring.

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Available abstract

Let be a commutative ring and a strictly totally ordered monoid.In this paper we prove that the ring [[ ]] of generalized power series is a strongly ring if and only if is a strongly ring and every -indexed subset of (the set of all idempotents of )has a least upper bound in ,and if also satisfied the condition that for any .then the ring [[ ]] is weakly ring if and only if is weakly ring.

Key concepts: Ring (chemistry), Mathematics, Principal ideal ring, Reduced ring, Noncommutative ring, Primitive ring, Boolean ring, Commutative ring

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