Algebras of right ample semigroups
Strict RA semigroups are common generalizations of ample semigroups and inverse semigroups. The aim of this paper is to study algebras of strict RA semigroups. It is proved that any algebra of strict RA semigroups with finite idempotents has a generalized matrix representation whose degree is equal...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-08-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2018-0075 |
| _version_ | 1819290960684646400 |
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| author | Guo Junying Guo Xiaojiang |
| author_facet | Guo Junying Guo Xiaojiang |
| author_sort | Guo Junying |
| collection | DOAJ |
| description | Strict RA semigroups are common generalizations of ample semigroups and inverse semigroups. The aim of this paper is to study algebras of strict RA semigroups. It is proved that any algebra of strict RA semigroups with finite idempotents has a generalized matrix representation whose degree is equal to the number of non-zero regular 𝓓-classes. In particular, it is proved that any algebra of finite right ample semigroups has a generalized upper triangular matrix representation whose degree is equal to the number of non-zero regular 𝓓-classes. As its application, we determine when an algebra of strict RA semigroups (right ample monoids) is semiprimitive. Moreover, we prove that an algebra of strict RA semigroups (right ample monoids) is left self-injective iff it is right self-injective, iff it is Frobenius, and iff the semigroup is a finite inverse semigroup. |
| first_indexed | 2024-12-24T03:31:03Z |
| format | Article |
| id | doaj.art-2e096e39828d430db2961f064bcec73a |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-24T03:31:03Z |
| publishDate | 2018-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-2e096e39828d430db2961f064bcec73a2022-12-21T17:17:11ZengDe GruyterOpen Mathematics2391-54552018-08-0116184286110.1515/math-2018-0075math-2018-0075Algebras of right ample semigroupsGuo Junying0Guo Xiaojiang1College of Science and Technology, Jiangxi Normal University, Nanchang, Jiangxi 330027, ChinaCollege of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi 330022, ChinaStrict RA semigroups are common generalizations of ample semigroups and inverse semigroups. The aim of this paper is to study algebras of strict RA semigroups. It is proved that any algebra of strict RA semigroups with finite idempotents has a generalized matrix representation whose degree is equal to the number of non-zero regular 𝓓-classes. In particular, it is proved that any algebra of finite right ample semigroups has a generalized upper triangular matrix representation whose degree is equal to the number of non-zero regular 𝓓-classes. As its application, we determine when an algebra of strict RA semigroups (right ample monoids) is semiprimitive. Moreover, we prove that an algebra of strict RA semigroups (right ample monoids) is left self-injective iff it is right self-injective, iff it is Frobenius, and iff the semigroup is a finite inverse semigroup.https://doi.org/10.1515/math-2018-0075right ample semigroupsemigroup algebrageneralized (upper triangular) matrix representationleft self-injective algebrafrobenius algebra20m3016g60 |
| spellingShingle | Guo Junying Guo Xiaojiang Algebras of right ample semigroups Open Mathematics right ample semigroup semigroup algebra generalized (upper triangular) matrix representation left self-injective algebra frobenius algebra 20m30 16g60 |
| title | Algebras of right ample semigroups |
| title_full | Algebras of right ample semigroups |
| title_fullStr | Algebras of right ample semigroups |
| title_full_unstemmed | Algebras of right ample semigroups |
| title_short | Algebras of right ample semigroups |
| title_sort | algebras of right ample semigroups |
| topic | right ample semigroup semigroup algebra generalized (upper triangular) matrix representation left self-injective algebra frobenius algebra 20m30 16g60 |
| url | https://doi.org/10.1515/math-2018-0075 |
| work_keys_str_mv | AT guojunying algebrasofrightamplesemigroups AT guoxiaojiang algebrasofrightamplesemigroups |