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首页> 外文期刊>Journal of algebra and its applications >On n-absorbing and strongly n-absorbing ideals of amalgamation
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On n-absorbing and strongly n-absorbing ideals of amalgamation

机译：On n-absorbing and strongly n-absorbing ideals of amalgamation

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Let R be a commutative ring with 1 not equal 0. Let n >= 1 be a positive integer. A proper ideal I of R is called an n-absorbing ideal (respectively, a strongly n-absorbing ideal) of R as in [D. F. Anderson and A. Badawi, On n-absorbing ideals of commutative rings, Comm. Algebra 39 (2011) 1646-1672] if a(1), a(2), ..., a(n+1) is an element of R and a(1). a2 ... is an element of I, then there are n of the ai's whose product is in I (respectively, if whenever I-1 ... In+1 subset of I for ideals I-1, ..., In+1 of R, then the product of some n of the I-j's is contained in I). The concept of n-absorbing ideals is a generalization of the concept of prime ideals (note that a prime ideal of R is a 1-absorbing ideal of R). Let f : A -> B be a ring homomorphism and let J be an ideal of B. This paper investigates the n-absorbing and strongly n-absorbing ideals in the amalgamation of A with B along J with respect f denoted by A (sic)(f) J. The obtained results generate new original classes of n-absorbing and strongly n-absorbing ideals.

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