Almost distributive lattices
1981 ◽
Vol 31
(1)
◽
pp. 77-91
◽
Keyword(s):
AbstractThe 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, P1-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.
2010 ◽
Vol 03
(02)
◽
pp. 335-346
Keyword(s):
Keyword(s):
Keyword(s):
2011 ◽
Vol 04
(01)
◽
pp. 171-178
◽
Keyword(s):
2021 ◽
Vol 14
(3)
◽
pp. 207-217
1971 ◽
Vol 23
(5)
◽
pp. 866-874
◽
Keyword(s):
1975 ◽
Vol 19
(2)
◽
pp. 238-246
◽
Keyword(s):