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Injectives in some small varieties of Ockham algebras. (English) Zbl 0539.06013

An MS-algebra is an algebra \(<L,\wedge,\vee,\circ,0,1>\) of type \(<2,2,1,0,0>\) such that \(<L,\wedge,\vee,0,1>\) is a bounded distributive lattice and \(\circ\) is a unary operation on L such that \((x\wedge y)\circ =x\circ \vee y\circ,\quad x\leq x\circ \circ,\quad 1\circ =0.\) The lattice of subvarieties of the variety MS of MS-algebras, together with the subdirectly irreducible MS-algebras, have been described by the reviewer and J. C. Varlet. Here the author describes the injective algebras in each of the twenty subvarieties of MS.
Reviewer: T.S.Blyth

MSC:

06D30 De Morgan algebras, Łukasiewicz algebras (lattice-theoretic aspects)
06B20 Varieties of lattices
08B15 Lattices of varieties
08B30 Injectives, projectives
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References:

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