Congruences in partial abelian semigroups |
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Authors: | S Pulmannová |
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Institution: | (1) Mathematical Institute, Slovak Academy of Sciences, SK- 814 73 Bratislava,Slovakia. E-mail: , |
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Abstract: | A partial abelian semigroup (PAS) is a structure , where is a partial binary operation on L with domain , which is commutative and associative (whenever the corresponding elements exist). A class of congruences on partial abelian
semigroups are studied such that the corresponding quotient is again a PAS. If M is a subset of a PAS L, we say that are perspective with respect to M, if there is such that and A subset M is called weakly algebraic if perspectivity with respect to M is a congruence. Some conditions are shown under which a congruence coincides with a perspectivity with respect to an appropriate
set M. Especially, conditions under which the corresponding quotient is a D-poset are found. It is also shown that every congruence
of MV-algebras and orthomodular lattices is given by a perspectivity with respect to an appropriate set M.
Received July 17, 1995; accepted in final form September 16, 1996. |
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Keywords: | and phrases Partial abelian semigroup effect algebra difference (operation) on a poset orthomodular poset orthoalgebra difference poset homomorphism and congruence of partial abelian semigroups algebraic set |
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