Please use this identifier to cite or link to this item:
https://open.uns.ac.rs/handle/123456789/8128
DC Field | Value | Language |
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dc.contributor.author | Shao Y. | en_US |
dc.contributor.author | Crvenković, Sinisa | en_US |
dc.contributor.author | Mitrović, Melanija | en_US |
dc.date.accessioned | 2019-09-30T09:06:46Z | - |
dc.date.available | 2019-09-30T09:06:46Z | - |
dc.date.issued | 2013-12-01 | - |
dc.identifier.issn | 14467887 | en_US |
dc.identifier.uri | https://open.uns.ac.rs/handle/123456789/8128 | - |
dc.description.abstract | A semiring is a set S with two binary operations + and · such that both the additive reduct S+ and the multiplicative reduct S• are semigroups which satisfy the distributive laws. If R is a ring, then, following Chaptal ['Anneaux dont le demi-groupe multiplicatif est inverse', C. R. Acad. Sci. Paris Ser. A-B 262 (1966), 274-277], R• is a union of groups if and only if R• is an inverse semigroup if and only if R• is a Clifford semigroup. In Zeleznikow ['Regular semirings', Semigroup Forum 23 (1981), 119-136], it is proved that if R is a regular ring then R• is orthodox if and only if R• is a union of groups if and only if R• is an inverse semigroup if and only if R• is a Clifford semigroup. The latter result, also known as Zeleznikow's theorem, does not hold in general even for semirings S with S+ a semilattice Zeleznikow ['Regular semirings', Semigroup Forum 23 (1981), 119-136]. The Zeleznikow problem on a certain class of semirings involves finding condition(s) such that Zeleznikow's theorem holds on that class. The main objective of this paper is to solve the Zeleznikow problem for those semirings S for which S+ is a semilattice. © 2013 Australian Mathematical Publishing Association Inc. | en_US |
dc.relation.ispartof | Journal of the Australian Mathematical Society | en_US |
dc.title | The Zeleznikow problem on a class of additively idempotent semirings | en_US |
dc.type | Journal/Magazine Article | en_US |
dc.identifier.doi | 10.1017/S1446788713000359 | - |
dc.identifier.scopus | 2-s2.0-84893648372 | - |
dc.identifier.url | https://api.elsevier.com/content/abstract/scopus_id/84893648372 | - |
dc.description.version | Unknown | en_US |
dc.relation.lastpage | 420 | en_US |
dc.relation.firstpage | 404 | en_US |
dc.relation.issue | 3 | en_US |
dc.relation.volume | 95 | en_US |
item.grantfulltext | none | - |
item.fulltext | No Fulltext | - |
Appears in Collections: | PMF Publikacije/Publications |
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