ON PRIMENESS OF PATH ALGEBRAS OVER A UNITAL COMMUTATIVE RING
| Main Authors: | Wardati, Khurul, Wijayanti, Indah, Wahyuni, Sri |
|---|---|
| Format: | Article PeerReviewed Book |
| Bahasa: | eng |
| Terbitan: |
Pushpa Publishing House
, 2014
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| Subjects: | |
| Online Access: |
http://digilib.uin-suka.ac.id/37246/1/JPANTA-2014-SCOPUS-an.KHURUL.pdf http://digilib.uin-suka.ac.id/37246/ http://pphmj.com/journals/jpanta.htm |
Daftar Isi:
- 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.