ON PRIMARY IDEALS OF POINTFREE FUNCTION RINGS

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Abedi Mostafa

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Journal Paper

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Journal: JOURNAL OF ALGEBRAIC SYSTEMS Year:2020 | Volume:7 | Issue:2 Page(s): 257-269

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Information Journal Paper

Title

ON PRIMARY IDEALS OF POINTFREE FUNCTION RINGS

Author(s)

Abedi Mostafa | Issue Writer Certificate

Keywords

Frame

primary ideal

pseudo-prime ideal

ring of continuous real-valued functions

decomposable ideal

Abstract

We study primary ideals of the ring RLRL of real-valued continuous functions on a completely regular Frame LL. We observe that prime ideals and primary ideals coincide in a PP-Frame. It is shown that every primary ideal in RLRL is contained in a unique maximal ideal, and an ideal QQ in RLRL is primary if and only if Q∩ R∗ LQ∩ R∗ L is a primary ideal in R∗ LR∗ L. We show that every pseudo-prime (primary) ideal in RLRL is either an essential ideal or a maximal ideal which is at the same time a minimal prime ideal. Finally, we prove that if LL is a connected Frame, then the zero ideal in RLRL is decomposable if and only if L=2L=2.

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APA: Copy

Abedi, Mostafa. (2020). ON PRIMARY IDEALS OF POINTFREE FUNCTION RINGS. JOURNAL OF ALGEBRAIC SYSTEMS, 7(2 ), 257-269. SID. https://sid.ir/paper/268359/en

Vancouver: Copy

Abedi Mostafa. ON PRIMARY IDEALS OF POINTFREE FUNCTION RINGS. JOURNAL OF ALGEBRAIC SYSTEMS[Internet]. 2020;7(2 ):257-269. Available from: https://sid.ir/paper/268359/en

IEEE: Copy

Mostafa Abedi, “ON PRIMARY IDEALS OF POINTFREE FUNCTION RINGS,” JOURNAL OF ALGEBRAIC SYSTEMS, vol. 7, no. 2 , pp. 257–269, 2020, [Online]. Available: https://sid.ir/paper/268359/en

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