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Almost distributive lattices
| Content Provider | Scilit |
|---|---|
| Author | Swamy, U. Maddana Rao, G. C. |
| Copyright Year | 1981 |
| Description | The concept of ‘Almost Distributive Lattices’ (ADL) is introduced. This class of ADLs includes almost all the existing ring theoretic generalisations of a Boolean ring (algebra) like regular rings, P-rings, biregular rings, associate rings, $P_{1}$-rings, triple systems, etc. This class also includes the class of Baer-Stone semigroups. A one-to-one correspondence is exhibited between the class of relatively complemented ADLs and the class of Almost Boolean Rings analogous to the well-known Stone's correspondence. Many concepts in distributive lattices can be extended to the class of ADLs through its principal ideals which from a distributive lattice with 0. Subdirect and Sheaf representations of an ADL are obtained. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/DDD1AB963A3E866940FEABC523C6001F/S1446788700018498a.pdf/div-class-title-almost-distributive-lattices-div.pdf |
| Ending Page | 91 |
| Page Count | 15 |
| Starting Page | 77 |
| ISSN | 02636115 |
| DOI | 10.1017/s1446788700018498 |
| Journal | Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics |
| Issue Number | 1 |
| Volume Number | 31 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1981-06-01 |
| Access Restriction | Open |
| Subject Keyword | Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics History and Philosophy of Science Distributive Lattice |
| Content Type | Text |
| Resource Type | Article |
