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A principal ideal theorem analogue for modules over commutative rings

1994; Taylor & Francis; Volume: 22; Issue: 6 Linguagem: Inglês

10.1080/00927879408824957

1532-4125

Seleena M. George, Roy McCasland, Patrick F. Smith,

Commutative Algebra and Its Applications

The Principal Ideal Theorem states that if Re is a commutative Noetherian ring and ? is a prime ideal of Re which is minimal over a principal ideal then Pe has height at most 1. Also, if Re is a (not necessarily Noetherian) UFD and Pe is a prime ideal of Re minimal over a principal ideal then Pe has height at most 1. We shall show that there are analogues for modules over commutative rings, but they hold only in special cases.