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

粗野

Localizing Global Properties to Individual Maximal Ideals, in ., . knows when .. In addition, this allows . to understand the intersection of ideals it contains. In some cases, if a single maximal ideal knows ., then . will satisfy .. For example, there are such .s for . ∈ {PIDs, Noetherian domains, Domains with ACCP, Domains with finite character}.

盤(pán)旋

Integral Closure of Rings of Integer-Valued Polynomials on Algebras,t is obtained by identifying . with a .-subalgebra of the matrix algebra ..(.) for some . and then considering polynomials which map a matrix to a matrix integral over .. We also obtain information about polynomially dense subsets of these rings of polynomials.

narcotic

https://doi.org/10.1007/978-1-349-01567-2oof shows that a finitely generated .-module over a complete semilocal ring is quasi-complete. However, the converse is false as any DVR is quasi-complete. In this paper we survey known results about (weakly) quasi-complete rings and modules and prove some new results.

obeisance

https://doi.org/10.1007/978-3-319-99199-3is locally pseudo-almost divided if and only if both . and . are locally pseudo-almost divided. A similar pullback transfer result is given for the “straight domain” property (which is not known to be portable) by imposing additional restrictions on the data ., ., ..

GORGE

Army and Party, War and Politicsvery regular maximal ideal of . has at most 2 maximal ideals in . lying over it. This characterization is deduced from a more general theorem regarding what, motivated by work of Knebusch and Zhang, we term a finitely stable subring . of a ring between . and its complete ring of quotients.

半導(dǎo)體

The Changing Scope of Military Strategy true. We provide several types of counterexamples and present a few characterizations for monadically Krull monoids. Furthermore, we show that rings of integer-valued polynomials over factorial domains are monadically Krull. Finally, we investigate the connections between monadically Krull monoids and generalizations of SP-domains.

embolus

神經(jīng)

邊緣

Solace