On a common abstraction of Boolean rings and lattice ordered groups II
- 1 March 1972
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 13 (2) , 185-195
- https://doi.org/10.1017/s1446788700011265
Abstract
In an earlier paper, the author has obtained a solution [8] to Birkhoff's problem No. 105 [1]: Is there a common abstraction which includes Boolean algebras (Rings) and lattice ordered groups as special cases? The solution actually turns out to be the direct product of a Boolean ring and a lattice ordered group. Birkhoff's problem has also been solved by Swamy, Wyler, and Nakano by presenting respectively i) Dually Residuated Lattice Ordered Semigroups (D.R.1. semigroups) [2, 3, 4, 5], ii) Clans [6], and iii) Multirings [7].Keywords
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