General ZPI-rings without Identity

• Autores: D. D. Anderson, John S. Kintzinger
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 33, Nº 3, 2007, págs. 631-634
• Idioma: inglés
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• Resumen

  • General ZPI-rings without IdentityLet R be a commutative ring not necessarily having an identity. Then R is a general ZPI-ring if every ideal of R is a product of prime ideals. S. Mori showed that a general ZPI-ring without identity is either (1) an integral domain, (2) a ring R where every ideal of R including 0 is a power of R, (3) K times R where K is a field and R is a ring as in (2), or (4) K times D where K is a field and D is a domain with every nonzero ideal of D a power of D. The purpose of this paper is to prove that if R is a ring as in (2), then there is an SPIR S with S=R[1] having R as its maximal ideal. Moreover, there is a complete DVR (D,(p)) with D=(p)[1] so that S and R are homomorphic images of D and (p), respectively.