On Maximal Subsemigroups of Partial Baer-Levi Semigroups
Suppose that X is an infinite set with |X|≥q≥ℵ0 and I(X) is the symmetric inverse semigroup defined on X. In 1984, Levi and Wood determined a class of maximal subsemigroups MA (using certain subsets A of X) of the Baer-Levi semigroup BL(q)={α∈I(X): dom α=X and |X∖Xα|=q}. Later, in 1995, Hotzel showe...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/489674 |
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| author | Boorapa Singha Jintana Sanwong |
| author_facet | Boorapa Singha Jintana Sanwong |
| author_sort | Boorapa Singha |
| collection | DOAJ |
| description | Suppose that X is an infinite set with |X|≥q≥ℵ0 and I(X) is the symmetric inverse semigroup defined on X. In 1984, Levi and Wood determined a class of maximal subsemigroups MA (using certain subsets A of X) of the Baer-Levi semigroup BL(q)={α∈I(X): dom α=X and |X∖Xα|=q}. Later, in 1995, Hotzel showed that there are many other classes of maximal subsemigroups of BL(q), but these are far more complicated to describe. It is known that BL(q) is a subsemigroup of the partial Baer-Levi semigroup PS(q)={α∈I(X):|X∖Xα|=q}. In this paper, we characterize all maximal subsemigroups of PS(q) when |X|>q, and we extend MA to obtain maximal subsemigroups of PS(q) when |X|=q. |
| format | Article |
| id | doaj-art-75f941f6d89a42ceb3b4bd06f4d03131 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-75f941f6d89a42ceb3b4bd06f4d031312025-02-03T01:09:32ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/489674489674On Maximal Subsemigroups of Partial Baer-Levi SemigroupsBoorapa Singha0Jintana Sanwong1Department of Mathematics, Chiang Mai University, Chiangmai 50200, ThailandDepartment of Mathematics, Chiang Mai University, Chiangmai 50200, ThailandSuppose that X is an infinite set with |X|≥q≥ℵ0 and I(X) is the symmetric inverse semigroup defined on X. In 1984, Levi and Wood determined a class of maximal subsemigroups MA (using certain subsets A of X) of the Baer-Levi semigroup BL(q)={α∈I(X): dom α=X and |X∖Xα|=q}. Later, in 1995, Hotzel showed that there are many other classes of maximal subsemigroups of BL(q), but these are far more complicated to describe. It is known that BL(q) is a subsemigroup of the partial Baer-Levi semigroup PS(q)={α∈I(X):|X∖Xα|=q}. In this paper, we characterize all maximal subsemigroups of PS(q) when |X|>q, and we extend MA to obtain maximal subsemigroups of PS(q) when |X|=q.http://dx.doi.org/10.1155/2011/489674 |
| spellingShingle | Boorapa Singha Jintana Sanwong On Maximal Subsemigroups of Partial Baer-Levi Semigroups International Journal of Mathematics and Mathematical Sciences |
| title | On Maximal Subsemigroups of Partial Baer-Levi Semigroups |
| title_full | On Maximal Subsemigroups of Partial Baer-Levi Semigroups |
| title_fullStr | On Maximal Subsemigroups of Partial Baer-Levi Semigroups |
| title_full_unstemmed | On Maximal Subsemigroups of Partial Baer-Levi Semigroups |
| title_short | On Maximal Subsemigroups of Partial Baer-Levi Semigroups |
| title_sort | on maximal subsemigroups of partial baer levi semigroups |
| url | http://dx.doi.org/10.1155/2011/489674 |
| work_keys_str_mv | AT boorapasingha onmaximalsubsemigroupsofpartialbaerlevisemigroups AT jintanasanwong onmaximalsubsemigroupsofpartialbaerlevisemigroups |