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International Conference on Ordered Algebraic Structures and Related Areas
July 6-10, 1998
Nanjing University
Nanjing, China

Organizers
W.C.Holland, P.Conrad, K.Denecke, M.Giraudet, A.C.Kim, V.Kopytov, N.Y.Medvedev, I.Rival, K.P.Shum, Dao-Rong Ton, C.Tsinakis, Minxie Jiang, Kaiyao He

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Annihilators in autometrized algebras
by
Jirí Rachunek
Palacky University Olomouc, Czech Republic
Coauthors: Ivan Chajda

An autometrized lattice algebra (Al-algebra) A is a lattice ordered commutative monoid endowed with a binary operation on A satisfying the properties of an autometric. We deal with the class of so-called normal Al-algebras (NAl-algebras) which contains as special cases all abelian lattice ordered groups and Brouwerian algebras. The concepts of annihilators and relative annihilators in NAl-algebras are introduced here. The connections between annihilators, relative annihilators, ideals and principal ideals are described. Further we introduce the notion of an I-polar of an NAl-algebra A for any ideal I of A and show that the polars and relative annihilators are special kinds of I-polars. The I-polars are recognized as the pseudocomplements in the Brouwerian lattice of all ideals of A containing I.

Date received: April 17, 1998

Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caba-06.