논문KCI 등재
ZPI Property In Amalgamated Duplication Ring
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Let A be a commutative ring. We say that A is a ZPI ring if every proper ideal of A is a finite product of prime ideals [5]. In this paper, we study when the amalgamated duplication of A along an ideal I, A I to be a ZPI ring. We show that if I is an idempotent ideal of A, then A is a ZPI ring if and only if A I is a ZPI ring.
Abstract
Let A be a commutative ring. We say that A is a ZPI ring if every proper ideal of A is a finite product of prime ideals [5]. In this paper, we study when the amalgamated duplication of A along an ideal I, A I to be a ZPI ring. We show that if I is an idempotent ideal of A, then A is a ZPI ring if and only if A I is a ZPI ring.
참고문헌 (9)
- M. D’Anna, "Properties of chains of prime ideal of amalgamated algebra along an ideal", J. Pure Appl. Algebra, 214(9), pp.1633~1641 (2010)
- M. D’Anna, "Commutative algebra and its applications", pp.155~172
- M. D’Anna, "A construction of Gorenstein rings", J. Algebra, 306(2), pp.507~519 (2006)
- M. D’Anna, "The amalgamated duplication of ring along an ideal: the basic properties", J. Algebra Appl, 6, pp.241~252 (2007)
- H. S. Butts, "Primary ideals and prime power ideals", Canadian J. Math, 18, pp.1183~1195 (1966)
- "Comm. Algebra", 2015, 3848~3856
- M. Larsen, "Multiplicative theory of ideals, Pure and Applied Math-ematics" (1971), Academic Press
- K. B. Levitz, "A Charecterization of General Z.P.I−Rings", Proc. Amer. Math. Soc, 32(2), pp.376~380 (1972)
- C. A. Wood, "On General Z.P.I-Rings", Pacific J. Math, 30(3), pp.837~846 (1969)
관련 논문AI추천
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