Chiang Mai Journal of Science

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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

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