Multiplicative closure operations on ring extensions

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:225

Article

Spirito, Dario^1,2 

[1] Univ Roma Tre, Dipartimento Matemat & Fis, Rome, Italy

[2] Univ Padua, Dipartimento Matemat Tullio Levi Civita, Padua, Italy

关键词: Closure operations;    Star operations;    Semiprime operations;    Ring extensions;   

DOI  :  10.1016/j.jpaa.2020.106555

来源: Elsevier

【 摘 要 】

Let A subset of B be a ring extension and G be a set of A-submodules of B. We introduce a class of closure operations on G (which we call multiplicative operations on (A, B, G)) that generalizes the classes of star, semistar and semiprime operations. We study how the set Mult(A, B, G) of these closure operations varies when A, B or G vary, and how Mult(A, B, G) behaves under ring homomorphisms. As an application, we show how to reduce the study of star operations on analytically unramified one-dimensional Noetherian domains to the study of closures on finite extensions of Artinian rings. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free