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- W1570961490 abstract "Let $D$ be a principal ideal domain and $R(D) = {begin{pmatrix} a & b 0 & a end{pmatrix} mid a, b in D}$ be its self-idealization. It is known that $R(D)$ is a commutative noetherian ring with identity, and hence $R(D)$ is atomic (i.e., every nonzero nonunit can be written as a finite product of irreducible elements). In this paper, we completely characterize the irreducible elements of $R(D)$. We then use this result to show how to factorize each nonzero nonunit of $R(D)$ into irreducible elements. We show that every irreducible element of $R(D)$ is a primary element, and we determine the system of sets of lengths of $R(D)$." @default.
- W1570961490 created "2016-06-24" @default.
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- W1570961490 date "2013-11-20" @default.
- W1570961490 modified "2023-09-23" @default.
- W1570961490 title "Factorization in the self-idealization of a PID" @default.
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