%0 Journal Article
%@ 0972-5555
%A Wardati, Khurul
%A Wijayanti, Indah
%A Wahyuni, Sri
%D 2014
%F digilib:37246
%I Pushpa Publishing House
%J JP Journal of Algebra, Number Theory and Applications
%K PRIMENESS, PATH ALGEBRAS OVER A  UNITAL COMMUTATIVE RING
%N 2
%P 121-138
%T ON PRIMENESS OF PATH ALGEBRAS OVER A  UNITAL COMMUTATIVE RING
%U https://digilib.uin-suka.ac.id/id/eprint/37246/
%V 34
%X 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.