整环上广义幂级数环的分解性质

FACTORIZATION IN RINGS OF GENERALIZED POWER SERIES OVER INTEGRAL DOMAINS

设A■B是整环的扩张, (S,≤)是满足一定条件的严格偏序幺半群, [[BS,≤]]是整环B上的广义幂级数环.本文研究整环[[BS,≤]]和{f∈[[BS,≤]]|f(0)∈A}的ACCP条件和BFD性质. 结果表明,整环{f∈[[BS,≤]]|f(0)∈A}的分解性质不仅依赖于A和B的分解性质以及U(A)和U(B),而且还依赖于幺半群S的分解性质.该结果能够构造出具有某种分解性质的整环的新例子.

Let A belong to B be an extension of integral domains. The author studies the ACCP and BED properitse of the integral domains [[B^S,≤]] and {f∈[[B^S,≤]]｜f（0）∈A}, where （S,≤） is a strictly ordered monoid satisfies some additional conditions and [[B^S,≤]] is the ring of generalized power series over B. These factorization properies for {f∈[[B^S,≤]]｜f（0）∈A} depend not holy on factorization properties in A and B, and on U（A） and U（B）, but also on factorization properties in S. This result enables us to construct several new examples of these types of domains satisfying some factorization properties.