The Ohm Type Properties for Multiplication Ideals
نویسنده
چکیده
Let R be a commutative ring with identity. An ideal I in R is called a multiplication ideal if every ideal contained in I is a multiple of I. Ohm's properties for nitely generated ideals in Pr ufer domains are investigated by Gilmer. These properties are generalized by Naoum and studied for nitely generated multiplication ideals. The purpose of this work is to generalize the results of Gilmer and Naoum to the case of multiplication ideals (not necessarily nitely generated ones). Let R be a ring. An ideal aR + bR is said to satisfy property (k) if (aR + bR) k = a k R + b k R for each positive integer k, see 6]. It is known that this property holds if aR + bR is invertible 6]. This property is extended for nitely generated cancellation ideals 5], nitely generated projective ideals 10] and 11], and for nitely generated multiplication ideals 9]. It is also shown in 6] that if I (2) is a collection of ideals in a Pr ufer domain R then X 2
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