Annihilators in Normal Autometrized Algebras |
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| Authors: | Ivan Chajda Jiri Rachunek |
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| Institution: | (1) Dept. of Algebra and Geometry, Palacky University, Tomkova 40, 779 00 Olomouc, Czech Republic |
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| Abstract: | The concepts of an annihilator and a relative annihilator in an autometrized l-algebra are introduced. It is shown that every relative annihilator in a normal autometrized l-algebra
is an ideal of
and every principal ideal of
is an annihilator of
. The set of all annihilators of
forms a complete lattice. The concept of an I-polar is introduced for every ideal I of
. The set of all I-polars is a complete lattice which becomes a two-element chain provided I is prime. The I-polars are characterized as pseudocomplements in the lattice of all ideals of
containing I. |
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| Keywords: | autometrized algebra annihilator relative annihilator ideal polar |
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