Relatively Orthocomplemented Skew Nearlattices in Rickart Rings
A class of (right) Rickart rings, called strong, is isolated. In particular, every Rickart *-ring is strong. It is shown in the paper that every strong Rickart ring R admits a binary operation which turns R into a right normal band having an upper bound property with respect to its natural order ≤;...
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| Format: | Article |
| Language: | English |
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De Gruyter
2015-12-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | http://www.degruyter.com/view/j/dema.2015.48.issue-4/dema-2015-0036/dema-2015-0036.xml?format=INT |
| _version_ | 1818566227120881664 |
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| author | Cīırulis Jānis |
| author_facet | Cīırulis Jānis |
| author_sort | Cīırulis Jānis |
| collection | DOAJ |
| description | A class of (right) Rickart rings, called strong, is isolated. In particular, every Rickart *-ring is strong. It is shown in the paper that every strong Rickart ring R admits a binary operation which turns R into a right normal band having an upper bound property with respect to its natural order ≤; such bands are known as right normal skew nearlattices. The poset (R, ≤) is relatively orthocomplemented; in particular, every initial segment in it is orthomodular. |
| first_indexed | 2024-12-14T01:51:03Z |
| format | Article |
| id | doaj.art-73f8730ba9384c19a4f7ac0abb5cc39c |
| institution | Directory Open Access Journal |
| issn | 0420-1213 2391-4661 |
| language | English |
| last_indexed | 2024-12-14T01:51:03Z |
| publishDate | 2015-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-73f8730ba9384c19a4f7ac0abb5cc39c2022-12-21T23:21:22ZengDe GruyterDemonstratio Mathematica0420-12132391-46612015-12-0148449350810.1515/dema-2015-0036dema-2015-0036Relatively Orthocomplemented Skew Nearlattices in Rickart RingsCīırulis Jānis0Institute of Mathematics and Computer Science University of Latvia, Raina B., 29, Rīga, Lv-1459, LatviaA class of (right) Rickart rings, called strong, is isolated. In particular, every Rickart *-ring is strong. It is shown in the paper that every strong Rickart ring R admits a binary operation which turns R into a right normal band having an upper bound property with respect to its natural order ≤; such bands are known as right normal skew nearlattices. The poset (R, ≤) is relatively orthocomplemented; in particular, every initial segment in it is orthomodular.http://www.degruyter.com/view/j/dema.2015.48.issue-4/dema-2015-0036/dema-2015-0036.xml?format=INTorthogonalityrelatively orthocomplemented posetrestrictive semigroupRickart ringright normal bandright-star orderskew nearlattice |
| spellingShingle | Cīırulis Jānis Relatively Orthocomplemented Skew Nearlattices in Rickart Rings Demonstratio Mathematica orthogonality relatively orthocomplemented poset restrictive semigroup Rickart ring right normal band right-star order skew nearlattice |
| title | Relatively Orthocomplemented Skew Nearlattices in Rickart Rings |
| title_full | Relatively Orthocomplemented Skew Nearlattices in Rickart Rings |
| title_fullStr | Relatively Orthocomplemented Skew Nearlattices in Rickart Rings |
| title_full_unstemmed | Relatively Orthocomplemented Skew Nearlattices in Rickart Rings |
| title_short | Relatively Orthocomplemented Skew Nearlattices in Rickart Rings |
| title_sort | relatively orthocomplemented skew nearlattices in rickart rings |
| topic | orthogonality relatively orthocomplemented poset restrictive semigroup Rickart ring right normal band right-star order skew nearlattice |
| url | http://www.degruyter.com/view/j/dema.2015.48.issue-4/dema-2015-0036/dema-2015-0036.xml?format=INT |
| work_keys_str_mv | AT ciırulisjanis relativelyorthocomplementedskewnearlatticesinrickartrings |