Unique Factorization in a Principal Right Ideal Domain
نویسندگان
چکیده
منابع مشابه
Finitely-generated modules over a principal ideal domain
Let R be a commutative ring throughout. Usually R will be an integral domain and even a principal ideal domain, but these assumptions will be made explicitly. Since R is commutative, there is no distinction between left, right and 2-sided ideals. In particular, for every ideal I we have a quotient ring R/I. F always denotes a field. Our goal is to prove the classification theorem for finitely-g...
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Last week, Ari taught you about one kind of “simple” (in the nontechnical sense) ring, specifically semisimple rings. These have the property that every module splits as a direct sum of simple modules (in the technical sense). This week, we’ll look at a rather different kind of ring, namely a principal ideal domain, or PID. These rings, like semisimple rings, have the property that every (finit...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1965
ISSN: 0002-9939
DOI: 10.2307/2034690