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On a common abstraction of De Morgan algebras and Stone algebras. (English) Zbl 0536.06013
An MS-algebra (a common abstraction of de Morgan and Stone algebras) is an algebra \((L,+,\cdot,{\mathbb{O}},0,1)\) such that \((L,+,\cdot,0,1)\) is a bounded distributive lattice, and \(x\to x\circ\) is a unary operation such that \(x\leq x\circ \circ\), \((x\cdot y)\circ =x\circ +y\circ, 1\circ =0\). The authors study ideals which are congruence kernels, prove that there are only nine non-isomorphic subdirectly irreducible MS-algebras, and give a complete description of these algebras.
Reviewer: V.Meskhi

MSC:
06D30 De Morgan algebras, Łukasiewicz algebras (lattice-theoretic aspects)
06B10 Lattice ideals, congruence relations
06D15 Pseudocomplemented lattices
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[1] Varlet, Bull. Soc. Roy. Sci. Liege 38 pp 101– (1969)
[2] Balbes, Distributive Lattices (1974)
[3] DOI: 10.1007/BF01836429 · Zbl 0395.06007 · doi:10.1007/BF01836429
[4] Matsumoto, J. Osaka Inst. Sci. Tech. 2 pp 97– (1950)
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