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- W173810272 abstract "This chapter presents concepts of transferable tolerances, which are generalizations of regular or weakly regular algebras introduced for congruences. Tolerances on algebras and varieties were investigated by numerous authors from various points of view. Apart from interesting problems in the intrinsic theory of tolerances, these relations can serve also as a suitable tool in solving some problems of congruences on algebras. Tolerance on an algebra A means a reflexive and symmetric binary relation on the support of A that has the substitution property with respect to all operations of A , which means that this relation is a subalgebra of A×A . The set of all tolerances on an algebra A forms an algebraic lattice LT ( A ) with respect to set inclusion. Hence, there exists a least tolerance on A containing a given subset S of A , which is denoted by T ( S ). An algebra A has transferable tolerances or congruences if for any elements a , b , and c of A , there exists an element d of A such that T ( a , b ) = T ( c , d ) or θ( a , b ) = θ( c , d ), respectively. A variety V has transferable tolerances or congruences if each A∈V has this property." @default.
- W173810272 created "2016-06-24" @default.
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- W173810272 date "1986-01-01" @default.
- W173810272 modified "2023-09-25" @default.
- W173810272 title "TRANSFERABLE TOLERANCES AND WEAKLY TOLERANCE REGULAR LATTICES" @default.
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- W173810272 doi "https://doi.org/10.1016/b978-0-444-87759-8.50007-9" @default.
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