Subdirect products of semirings
Bandelt and Petrich (1982) proved that an inversive semiring S is a subdirect product of a distributive lattice and a ring if and only if S satisfies certain conditions. The aim of this paper is to obtain a generalized version of this result. The main purpose of this paper however, is to investigate...
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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201003696 |
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| author | P. Mukhopadhyay |
| author_facet | P. Mukhopadhyay |
| author_sort | P. Mukhopadhyay |
| collection | DOAJ |
| description | Bandelt and Petrich (1982) proved that an inversive semiring S is a subdirect product of a distributive lattice and a ring if and only if S satisfies certain conditions. The aim of this paper is to obtain a generalized version of this result. The main purpose of this paper however, is to investigate, what new necessary and sufficient conditions need we impose on an inversive semiring, so that, in its aforesaid representation as a subdirect product, the ring involved can be gradually enriched to a field. Finally, we provide a construction of full E-inversive semirings, which are subdirect products of a semilattice
and a ring. |
| format | Article |
| id | doaj-art-463fc91f40354f7ebec63e83dfbd3bbe |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-463fc91f40354f7ebec63e83dfbd3bbe2025-02-03T01:24:34ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0126953954510.1155/S0161171201003696Subdirect products of semiringsP. Mukhopadhyay0Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Calcutta 700019, IndiaBandelt and Petrich (1982) proved that an inversive semiring S is a subdirect product of a distributive lattice and a ring if and only if S satisfies certain conditions. The aim of this paper is to obtain a generalized version of this result. The main purpose of this paper however, is to investigate, what new necessary and sufficient conditions need we impose on an inversive semiring, so that, in its aforesaid representation as a subdirect product, the ring involved can be gradually enriched to a field. Finally, we provide a construction of full E-inversive semirings, which are subdirect products of a semilattice and a ring.http://dx.doi.org/10.1155/S0161171201003696 |
| spellingShingle | P. Mukhopadhyay Subdirect products of semirings International Journal of Mathematics and Mathematical Sciences |
| title | Subdirect products of semirings |
| title_full | Subdirect products of semirings |
| title_fullStr | Subdirect products of semirings |
| title_full_unstemmed | Subdirect products of semirings |
| title_short | Subdirect products of semirings |
| title_sort | subdirect products of semirings |
| url | http://dx.doi.org/10.1155/S0161171201003696 |
| work_keys_str_mv | AT pmukhopadhyay subdirectproductsofsemirings |