On semilattices of groups whose arrows are epimorphisms
A q partial group is defined to be a partial group, that is, a strong semilattice of groups S=[E(S);Se,ϕe,f] such that S has an identity 1 and ϕ1,e is an epimorphism for all e∈E(S). Every partial group S with identity contains a unique maximal q partial group Q(S) such that (Q(S))1=S1. This Q operat...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/30673 |
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| author | M. El-Ghali M. Abdallah L. N. Gab-Alla Sayed K. M. Elagan |
| author_facet | M. El-Ghali M. Abdallah L. N. Gab-Alla Sayed K. M. Elagan |
| author_sort | M. El-Ghali M. Abdallah |
| collection | DOAJ |
| description | A q partial group is defined to be a partial group, that is, a
strong semilattice of groups S=[E(S);Se,ϕe,f] such that S has an identity 1 and ϕ1,e is an epimorphism for all e∈E(S). Every partial group S with identity contains a unique maximal q partial group Q(S) such that (Q(S))1=S1. This Q operation is proved to commute with Cartesian products and preserve normality. With Q extended to idempotent separating congruences on
S, it is proved that Q(ρK)=ρQ(K) for every normal K in S. Proper q partial groups are defined in such a way that associated to any group G, there is a proper
q partial group P(G) with (P(G))1=G. It is proved that a q partial group S is proper if and only if S≅P(S1) and hence that if S is any partial group, there exists a group M such that S is embedded in P(M). P epimorphisms of proper q partial groups are
defined with which the category of proper q partial groups is
proved to be equivalent to the category of groups and epimorphisms
of groups. |
| format | Article |
| id | doaj-art-20185f71994c46a6ba656ef1970b3f36 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-20185f71994c46a6ba656ef1970b3f362025-02-03T01:26:22ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/3067330673On semilattices of groups whose arrows are epimorphismsM. El-Ghali M. Abdallah0L. N. Gab-Alla1Sayed K. M. Elagan2Department of Mathematics, Faculty of Science, Menoufiya University, Shebin El-Kom 32511, EgyptDepartment of Mathematics, Faculty of Science, Menoufiya University, Shebin El-Kom 32511, EgyptDepartment of Mathematics, Faculty of Science, Menoufiya University, Shebin El-Kom 32511, EgyptA q partial group is defined to be a partial group, that is, a strong semilattice of groups S=[E(S);Se,ϕe,f] such that S has an identity 1 and ϕ1,e is an epimorphism for all e∈E(S). Every partial group S with identity contains a unique maximal q partial group Q(S) such that (Q(S))1=S1. This Q operation is proved to commute with Cartesian products and preserve normality. With Q extended to idempotent separating congruences on S, it is proved that Q(ρK)=ρQ(K) for every normal K in S. Proper q partial groups are defined in such a way that associated to any group G, there is a proper q partial group P(G) with (P(G))1=G. It is proved that a q partial group S is proper if and only if S≅P(S1) and hence that if S is any partial group, there exists a group M such that S is embedded in P(M). P epimorphisms of proper q partial groups are defined with which the category of proper q partial groups is proved to be equivalent to the category of groups and epimorphisms of groups.http://dx.doi.org/10.1155/IJMMS/2006/30673 |
| spellingShingle | M. El-Ghali M. Abdallah L. N. Gab-Alla Sayed K. M. Elagan On semilattices of groups whose arrows are epimorphisms International Journal of Mathematics and Mathematical Sciences |
| title | On semilattices of groups whose arrows are epimorphisms |
| title_full | On semilattices of groups whose arrows are epimorphisms |
| title_fullStr | On semilattices of groups whose arrows are epimorphisms |
| title_full_unstemmed | On semilattices of groups whose arrows are epimorphisms |
| title_short | On semilattices of groups whose arrows are epimorphisms |
| title_sort | on semilattices of groups whose arrows are epimorphisms |
| url | http://dx.doi.org/10.1155/IJMMS/2006/30673 |
| work_keys_str_mv | AT melghalimabdallah onsemilatticesofgroupswhosearrowsareepimorphisms AT lngaballa onsemilatticesofgroupswhosearrowsareepimorphisms AT sayedkmelagan onsemilatticesofgroupswhosearrowsareepimorphisms |