Geodesic
Annihilators in normal autometrized algebras
Czechoslovak Mathematical Journal, Tome 51 (2001) no. 1, pp. 111-120 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $\mathcal {A}$ is an ideal of $\mathcal {A}$ and every principal ideal of $\mathcal {A}$ is an annihilator of $\mathcal {A}$. The set of all annihilators of $\mathcal {A}$ forms a complete lattice. The concept of an $I$-polar is introduced for every ideal $I$ of $\mathcal {A}$. 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 $\mathcal {A}$ containing $I$.
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 $\mathcal {A}$ is an ideal of $\mathcal {A}$ and every principal ideal of $\mathcal {A}$ is an annihilator of $\mathcal {A}$. The set of all annihilators of $\mathcal {A}$ forms a complete lattice. The concept of an $I$-polar is introduced for every ideal $I$ of $\mathcal {A}$. 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 $\mathcal {A}$ containing $I$.
Classification : 06F05
Keywords: autometrized algebra; annihilator; relative annihilator; ideal; polar 
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     url = {http://geodesic.mathdoc.fr/item/CMJ_2001_51_1_a9/}
}
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Chajda, Ivan; Rachůnek, Jiří. Annihilators in normal autometrized algebras. Czechoslovak Mathematical Journal, Tome 51 (2001) no. 1, pp. 111-120. http://geodesic.mathdoc.fr/item/CMJ_2001_51_1_a9/

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