Titlebook: Commutative Algebra; Recent Advances in C Marco Fontana,Sophie Frisch,Sarah Glaz Book 2014 Springer Science+Business Media New York 2014 Gr

gruelling

ABIDE

Quasi-complete Semilocal Rings and Modules,ondition: given any descending chain of ideals . with ., for each positive integer . there exists an .. with .. A finitely generated .-module . is said to be (.) . if for any descending chain . of .-submodules of . (with .) and . ≥ 1, there exists an .. with .. An easy modification of Chevalley’s pr

尊敬

On the Total Graph of a Ring and Its Related Graphs: A Survey,ith vertices all elements of ., and two distinct vertices . and . are adjacent if and only if . + . ∈ .(.). This type of graphs has been studied by many authors. In this paper, we state many of the main results on the total graph of a ring and its related graphs.

CRP743

Prime Ideals in Polynomial and Power Series Rings over Noetherian Domains,ries. We include a new result that is related to current work of the authors [Celikbas et al., .; see . (preprint)]: Theorem 5.4 gives a general description of the prime spectra of the rings . and .[.][​[.]​]∕.′, where . and . are indeterminates over a one-dimensional Noetherian integral domain . an

专心

On a New Class of Integral Domains with the Portable Property,ch that .. ∈ .. Such domains are related to several known kinds of domains, such as divided domains and straight domains. It is shown that “locally pseudo-almost divided” is a portable property of domains. Hence, if . is a domain with a maximal ideal . and . is a subring of .∕., then the pullback .

Corral

The Probability That Int,(,) Is Free, of . is a subgroup of the class group of . generated by the well-known factorial ideals .! . of .. A . of Int(.) is a .-module basis consisting of one polynomial of each degree. It is well known that Int(.) has a regular basis if and only if the group PO(.) is trivial, if and only if the .-module I

Resection

组装

Stable Homotopy Theory, Formal Group Laws, and Integer-Valued Polynomials,laws. For several generalized homology theories certain values of the theories have a natural description as such algebras and since these values are the ones arising in the construction of the Adams-Novikov spectral sequence for computing stable homotopy groups these algebras and their homological

低位的人或事

How to Construct Huge Chains of Prime Ideals in Power Series Rings,als in the polynomial ring .[.] has length at most 2. + 1. For the power series ring .[​[.]​], there is however no similar upper bound on lengths of chains of its prime ideals. In fact, in some special cases, there may exist chains of prime ideals in .[​[.]​] with huge lengths (e.g., .) even if each