Arithmetic of Semigroup Semirings
We define semigroup semirings by analogy with group rings and semigroup rings. We study the arithmetic properties and determine sufficient conditions under which a semigroup semiring is atomic, has finite factorization, or has bounded factorization. We also present a semigroup-semiring analog (altho...
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| Date: | 2015 |
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| Main Author: | |
| Format: | Article |
| Language: | Russian |
| Published: |
Інститут математики НАН України
2015
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| Series: | Український математичний журнал |
| Subjects: | |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/165465 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Arithmetic of Semigroup Semirings / V. Ponomarenko // Український математичний журнал. — 2015. — Т. 67, № 2. — С. 213–229. — Бібліогр.: 15 назв. — рос. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We define semigroup semirings by analogy with group rings and semigroup rings. We study the arithmetic properties and determine sufficient conditions under which a semigroup semiring is atomic, has finite factorization, or has bounded factorization. We also present a semigroup-semiring analog (although not a generalization) of the Gauss lemma on primitive polynomials. |
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