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Almost Primal Ideals in Commutative Rings


Paper Type 
Contributed Paper
Title 
Almost Primal Ideals in Commutative Rings
Author 
Ahmad Y. Darani
Email 
yousefian@uma.ac.ir and youseffian@gmail.com
Abstract:
Let I be a proper ideal of a commutative ring R. An element a ∈ R is called almost prime to I provided that ra ∈ I − I2 (with r ∈ R) implies that r ∈ I. We denote by A(I ) the set of all elements of R that are not almost prime to I. I is called an almost primal ideal of R if the set A(I ) ∪ I2 forms an ideal of R. In this paper we first provide some results on almost primal ideals. We also study the relations among the primal ideals, weakly primal ideals and almost primal ideals of R. Keywords: almost prime ideal, primal ideal, weakly primal ideal, weakly prime ideal. Throughout, R will be a commutative ring with
Start & End Page 
161 - 165
Received Date 
2010-07-15
Revised Date 
Accepted Date 
2011-01-31
Full Text 
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Keyword 
almost prime ideal, Throughout, R will be a commutative ring with, primal ideal, weakly primal ideal
Volume 
Vol.38 No.2 (APRIL 2011)
DOI 
Citation 
Darani A.Y., Almost Primal Ideals in Commutative Rings, Chiang Mai J. Sci., 2011; 38(2): 161-165.
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