Dedekind semidomains

Peyman Nasehpour

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arXiv · 1907.07162

Dedekind semidomains

Peyman Nasehpour

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Abstract

We define Dedekind semidomains as semirings in which each nonzero fractional ideal is invertible. Then we find some equivalent condition for semirings to being Dedekind. For example, we prove that a Noetherian semidomain is Dedekind if and only if it is multiplication. Then we show that a subtractive Noetherian semidomain is Dedekind if and only if it is a $π$-semiring and each of it nonzero prime ideal is invertible. We also show that the maximum number of the generators of each ideal of a subtractive Dedekind semidomain is 2.

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BibTeX RIS

Peyman Nasehpour. 2019-07-16. Dedekind semidomains. https://arxiv.org/abs/1907.07162

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