P-SPACES AND ARTIN-REES PROPERTY

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AZARPANAH FARIBORZE; AFROOZ SOOSAN

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Journal: ADVANCES IN MATHEMATICAL MODELING Year:2012 | Volume:2 | Issue:1 Page(s): 61-76

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Title

P-SPACES AND ARTIN-REES PROPERTY

Author(s)

AZARPANAH FARIBORZE | AFROOZ SOOSAN | Issue Writer Certificate

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Abstract

In this article, we study the Artin-Rees property in C (X), in the rings of fractions of C (X) and in the factor rings of C (X). We show that C (X)/ (f) is an Artin-Rees ring if and only if Z (f) is an open P-space. A necessary and sufficient condition for the local rings of C(X) to be Artin-Rees rings is that each prime ideal in C(X) becomes minimal and it turns out that every local ring of C (X) is an Artin-Rees ring if and only if X is a P-space. Finally we have shown that whenever XZ (f) is dense C-embedded in X, then C (X) f is regular if and only if Xz (f) is a P-space.

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APA: Copy

AZARPANAH, FARIBORZE, & AFROOZ, SOOSAN. (2012). P-SPACES AND ARTIN-REES PROPERTY. ADVANCES IN MATHEMATICAL MODELING, 2(1), 61-76. SID. https://sid.ir/paper/243932/en

Vancouver: Copy

AZARPANAH FARIBORZE, AFROOZ SOOSAN. P-SPACES AND ARTIN-REES PROPERTY. ADVANCES IN MATHEMATICAL MODELING[Internet]. 2012;2(1):61-76. Available from: https://sid.ir/paper/243932/en

IEEE: Copy

FARIBORZE AZARPANAH, and SOOSAN AFROOZ, “P-SPACES AND ARTIN-REES PROPERTY,” ADVANCES IN MATHEMATICAL MODELING, vol. 2, no. 1, pp. 61–76, 2012, [Online]. Available: https://sid.ir/paper/243932/en

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