# On the Krull property in topological algebras

Commentationes Mathematicae (2006)

- Volume: 46, Issue: 2
- ISSN: 2080-1211

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topMarina Haralampidou. "On the Krull property in topological algebras." Commentationes Mathematicae 46.2 (2006): null. <http://eudml.org/doc/292217>.

@article{MarinaHaralampidou2006,

abstract = {We introduce Krull topological algebras. In particular, we characterize the Krull property in some special classes of topological algebras. Connections with the theory of semisimple annihilator $Q^\{\prime \}$-algebras are given. Relative to this, an investigation on the relationship between Krull and (weakly) regular (viz. modular) annihilator algebras is considered. Subalgebras of certain Krull algebras are also presented. Moreover, conditions are supplied under which the Krull (resp. $Q^\{\prime \}$-) property is preserved via algebra morphisms. As an application, we show that the quotient of a Krull $Q^\{\prime \}$-algebra, modulo a 2-sided ideal, is a topological algebra of the same type. Finally, we study the Krull property in a certain algebra-valued function topological algebra.},

author = {Marina Haralampidou},

journal = {Commentationes Mathematicae},

keywords = {Krull algebra; annihilator algebra; semisimple algebra; socle; $Q^\{\prime \}$-algebra; (D)-algebra; (weakly) regular annihilator algebra; (ortho)complemented algebra},

language = {eng},

number = {2},

pages = {null},

title = {On the Krull property in topological algebras},

url = {http://eudml.org/doc/292217},

volume = {46},

year = {2006},

}

TY - JOUR

AU - Marina Haralampidou

TI - On the Krull property in topological algebras

JO - Commentationes Mathematicae

PY - 2006

VL - 46

IS - 2

SP - null

AB - We introduce Krull topological algebras. In particular, we characterize the Krull property in some special classes of topological algebras. Connections with the theory of semisimple annihilator $Q^{\prime }$-algebras are given. Relative to this, an investigation on the relationship between Krull and (weakly) regular (viz. modular) annihilator algebras is considered. Subalgebras of certain Krull algebras are also presented. Moreover, conditions are supplied under which the Krull (resp. $Q^{\prime }$-) property is preserved via algebra morphisms. As an application, we show that the quotient of a Krull $Q^{\prime }$-algebra, modulo a 2-sided ideal, is a topological algebra of the same type. Finally, we study the Krull property in a certain algebra-valued function topological algebra.

LA - eng

KW - Krull algebra; annihilator algebra; semisimple algebra; socle; $Q^{\prime }$-algebra; (D)-algebra; (weakly) regular annihilator algebra; (ortho)complemented algebra

UR - http://eudml.org/doc/292217

ER -

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