By Marco Fontana, Salah-Eddine Kabbaj, Bruce Olberding, Irena Swanson

ISBN-10: 311020746X

ISBN-13: 9783110207460

This quantity comprises chosen refereed papers in line with lectures awarded on the ??;Fifth foreign Fez convention on Commutative Algebra and Applications?? that used to be held in Fez, Morocco in June 2008. the amount represents new traits and components of classical study in the box, with contributions from many alternative international locations. furthermore, the amount has as a different concentration the learn and effect of Alain Bouvier on commutative algebra during the last thirty years.

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**Additional resources for Commutative Algebra and its Applications (De Gruyter Proceedings in Mathematics)**

**Example text**

On -divisorial ideals. The following is a characterization of -Mori rings in terms of Mori rings in the sense of [46]. 34 A. 2]). Let R 2 H . R/ is a Mori ring. The following is a characterization of -Mori rings in terms of Mori domains. 5]). Let R 2 H . R/ is a Mori domain. 7]). Let R 2 H be a -Mori ring. c. on nonnil divisorial ideals of R. In particular, R is a Mori ring. 3 is not valid as it can be seen by the following example. 8]). L=D/, the idealization of L=D over D. Then R 2 H is a Mori ring which is not a -Mori ring.

Let R 2 H be a -Mori ring and I be a nonzero -divisorial ideal of R. Then I contains a power of its radical. We recall a few definitions regarding special types of ideals in integral domains. II 1 /v D D. We will extend these concepts to the rings in H . Let I be a nonnil ideal of a ring R 2 H . II 1 /v D R 36 A. Badawi and -v-invertible if . R/. I / is, respectively, strong, strongly divisorial or v-invertible. In [51, Proposition 1], J. Querré proved that if P is a prime ideal of a Mori domain D, then P is divisorial when it is height one.

Let R 2 H . R/ is ring-isomorphic to a ring A obtained from the following pullback diagram: A # T ! A=M # ! T =M where T is a zero-dimensional quasilocal ring with maximal ideal M , A=M is a ZPUI ring that is a subring of T =M , the vertical arrows are the usual inclusion maps, and the horizontal arrows are the usual surjective maps. 7 -Krull rings We say that a ring R 2 H is a discrete -chained ring if R is a -chained ring with at most one nonnil prime ideal and every nonnil ideal of R is principal.

### Commutative Algebra and its Applications (De Gruyter Proceedings in Mathematics) by Marco Fontana, Salah-Eddine Kabbaj, Bruce Olberding, Irena Swanson

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