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Baer semigroup coordinatizations of modular lattices*
Published online by Cambridge University Press: 14 November 2011
Synopsis
In the coordinatization of lattices by Baer semigroups, two notable gaps that remain to be filled concern the coordinatization of modular and distributive lattices. In this paper we present coordinatizations of modular lattices. In a subsequent paper we shall deal with the distributive case. Here we show that a bounded lattice L is modular if and only if L can be coordinatized by a Baer semigroup S such that if eS, fS ∊ R(S) then there exist idempotents ē, ∊ S such that ēS = eS, S = fS and e¯, commute; equivalently, if and only if L can be coordinatized by a Baer semigroup S such that if eS, fS ∊ R(S) with e idempotent then there is an idempotent such that S = fS and e = ee.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 81 , Issue 1-2 , 1978 , pp. 49 - 56
- Copyright
- Copyright © Royal Society of Edinburgh 1978
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