TY - JOUR
ID - 1594
TI - ON PRIMARY IDEALS OF POINTFREE FUNCTION RINGS
JO - Journal of Algebraic Systems
JA - JAS
LA - en
SN - 2345-5128
AU - Abedi, M.
AD - Esfarayen University of Technology, Esfarayen, North Khorasan, Iran.
Y1 - 2020
PY - 2020
VL - 7
IS - 2
SP - 257
EP - 269
KW - Frame
KW - primary ideal
KW - pseudo-prime ideal
KW - ring of continuous real-valued functions
KW - decomposable ideal
DO - 10.22044/jas.2019.8150.1399
N2 - We study primary ideals of the ring $mathcal{R}L$ of real-valued continuous functions on a completely regular frame $L$. We observe that prime ideals and primary ideals coincide in a $P$-frame. It is shown that every primary ideal in $mathcal{R}L$ is contained in a unique maximal ideal, and an ideal $Q$ in $mathcal{R}L$ is primary if and only if $Q capmathcal{R}^*L$ is a primary ideal in $mathcal{R}^*L$. We show that every pseudo-prime (primary) ideal in $mathcal{R}L$ is either an essential ideal or a maximal ideal which is at the same time a minimal prime ideal. Finally, we prove that if $L$ is a connected frame, then the zero ideal in $mathcal{R}L$ is decomposable if and only if $L={bf2}$.
UR - http://jas.shahroodut.ac.ir/article_1594.html
L1 - http://jas.shahroodut.ac.ir/article_1594_8108dcd6f42553890dfb9b0ba2055003.pdf
ER -