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- W4254795303 abstract "Publisher SummaryAlthough classical matrix theory is concerned with matrices over the ring of integers Z or over a field, there are definite advantages to be gained by adopting a more general approach and studying matrices over any principal ideal ring. This chapter develops the properties of principal ideal rings that do not differ markedly from the properties of Z. A principal ideal ring R is a commutative ring with no zero divisors and a unit element 1 such that every ideal is principal, that is, such that every ideal consists of the totality of multiples of a fixed element. One of the most interesting conclusions to be drawn about principal ideal rings is that such a ring admits a theory of unique factorization. The chapter discusses euclidean rings. Every euclidean ring is itself a principal ideal ring but is not conversely. That is, there do exist principal deal rings that are not euclidean." @default.
- W4254795303 created "2022-05-12" @default.
- W4254795303 date "1972-01-01" @default.
- W4254795303 modified "2023-09-27" @default.
- W4254795303 title "Chapter I Background material on Rings" @default.
- W4254795303 doi "https://doi.org/10.1016/s0079-8169(08)62349-1" @default.
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