52 research outputs found
Interior and closure operators on bounded residuated lattice ordered monoids
summary:-algebras endowed with additive closure operators or with its duals-multiplicative interior operators (closure or interior -algebras) were introduced as a non-commutative generalization of topological Boolean algebras. In the paper, the multiplicative interior and additive closure operators on -monoids are introduced as natural generalizations of the multiplicative interior and additive closure operators on -algebras
Epimorphisms in varieties of subidempotent residuated structures
A commutative residuated lattice A is said to be subidempotent if the lower
bounds of its neutral element e are idempotent (in which case they naturally
constitute a Brouwerian algebra A*). It is proved here that epimorphisms are
surjective in a variety K of such algebras A (with or without involution),
provided that each finitely subdirectly irreducible algebra B in K has two
properties: (1) B is generated by lower bounds of e, and (2) the poset of prime
filters of B* has finite depth. Neither (1) nor (2) may be dropped. The proof
adapts to the presence of bounds. The result generalizes some recent findings
of G. Bezhanishvili and the first two authors concerning epimorphisms in
varieties of Brouwerian algebras, Heyting algebras and Sugihara monoids, but
its scope also encompasses a range of interesting varieties of De Morgan
monoids
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