%A Khurul Wardati
%A Indah Wijayanti
%A Sri Wahyuni
%J JP Journal of Algebra, Number Theory and Applications
%T ON PRIMENESS OF PATH ALGEBRAS OVER A
UNITAL COMMUTATIVE RING
%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.
%N 2
%K PRIMENESS, PATH ALGEBRAS OVER A
UNITAL COMMUTATIVE RING
%P 121-138
%V 34
%D 2014
%I Pushpa Publishing House
%L digilib37246