Annihilators in normal autometrized algebras
Czechoslovak Mathematical Journal (2001)
- Volume: 51, Issue: 1, page 111-120
- ISSN: 0011-4642
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topChajda, Ivan, and Rachůnek, Jiří. "Annihilators in normal autometrized algebras." Czechoslovak Mathematical Journal 51.1 (2001): 111-120. <http://eudml.org/doc/30618>.
@article{Chajda2001,
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 $\mathcal \{A\}$ 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 $I$.},
author = {Chajda, Ivan, Rachůnek, Jiří},
journal = {Czechoslovak Mathematical Journal},
keywords = {autometrized algebra; annihilator; relative annihilator; ideal; polar; autometrized algebra; annihilator; relative annihilator; ideal; polar},
language = {eng},
number = {1},
pages = {111-120},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Annihilators in normal autometrized algebras},
url = {http://eudml.org/doc/30618},
volume = {51},
year = {2001},
}
TY - JOUR
AU - Chajda, Ivan
AU - Rachůnek, Jiří
TI - Annihilators in normal autometrized algebras
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 1
SP - 111
EP - 120
AB - 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 $I$.
LA - eng
KW - autometrized algebra; annihilator; relative annihilator; ideal; polar; autometrized algebra; annihilator; relative annihilator; ideal; polar
UR - http://eudml.org/doc/30618
ER -
References
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