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primary topic: ON PRIMENESS OF PATH ALGEBRAS OVER A UNITAL COMMUTATIVE RING

ON PRIMENESS OF PATH ALGEBRAS OVER A UNITAL COMMUTATIVE RING
type: AcademicArticle
type: Article
abstract: In this paper, we first discuss the primeness of basic ideals in a free R-algebra where R is a unital commutative ring. The condition of primeness is applied to show a prime basic ideal in a path algebra RE on a graph E. For every hereditary subset H, we can construct a (graded) basic ideal IH in RE. The basic ideal IH is an ideal of linear combinations of vertices in H and paths whose ranges in H. The main purpose of this paper is to present the necessary and sufficient conditions on a graph, so that IH is a prime basic ideal, if H is saturated hereditary. Since ∅ is saturated hereditary, we find the necessary and sufficient conditions on a graph, so that a path algebra RE is basically prime.
date: 2014-10
volume: 34
issue: 2
is part of: JP Journal of Algebra, Number Theory and Applications
status: peerReviewed
status: published
author list: authors
type: EPrint
type: ArticleEPrint
is part of: repository
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subject: Matematika

ON PRIMENESS OF PATH ALGEBRAS OVER A UNITAL COMMUTATIVE RING (Text)
type: Document
has file: JPANTA-2014-SCOPUS-an.KHURUL.pdf
has part: JPANTA-2014-SCOPUS-an.KHURUL.pdf

Pushpa Publishing House
type: Organization

JP Journal of Algebra, Number Theory and Applications
type: Collection
issn: 09725555

Sri Wahyuni
type: Person
given name: Sri
family name: Wahyuni

Indah Wijayanti
type: Person
given name: Indah
family name: Wijayanti

Khurul Wardati
type: Person
given name: Khurul
family name: Wardati

ON PRIMENESS OF PATH ALGEBRAS OVER A UNITAL COMMUTATIVE RING (Other)
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ON PRIMENESS OF PATH ALGEBRAS OVER A UNITAL COMMUTATIVE RING (Other)
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primary topic: ON PRIMENESS OF PATH ALGEBRAS OVER A UNITAL COMMUTATIVE RING

Matematika
type: Concept