TY  - JOUR
ID  - digilib37246
UR  - http://pphmj.com/journals/jpanta.htm
IS  - 2
A1  - Wardati, Khurul
A1  - Wijayanti, Indah
A1  - Wahyuni, Sri
N2  - 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.
VL  - 34
TI  - ON PRIMENESS OF PATH ALGEBRAS OVER A
UNITAL COMMUTATIVE RING
AV  - public
EP  - 138
Y1  - 2014/10//
PB  - Pushpa Publishing House
JF  - JP Journal of Algebra, Number Theory and Applications
KW  - PRIMENESS
KW  -  PATH ALGEBRAS OVER A
UNITAL COMMUTATIVE RING
SN  - 0972-5555
SP  - 121
ER  -