有限生成投影模的清洁余代数和清洁余模

IF 0.3 Q4 MATHEMATICS, APPLIED Algebra & Discrete Mathematics Pub Date : 2021-07-19 DOI:10.12958/ADM1415

N. P. Puspita, I. E. Wijayanti, B. Surodjo

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引用次数: 2

摘要

设R是一个具有乘法恒等式的交换环，P是一个有限生成的射影R模。若P∗是由P到R的R模同态的集合，则张量积P∗⊗RP可以认为是一个R-协代数。更进一步，P和P *是协代数P *⊗RP上的一个微模。利用Morita上下文，给出了干净协代数P∗⊗RP和干净P∗⊗RP-模P和P∗的充分条件。这些充分条件由模P和环R的条件决定。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Clean coalgebras and clean comodules of finitely generated projective modules

Let R be a commutative ring with multiplicative identity and P is a finitely generated projective R-module. If P∗ is the set of R-module homomorphism from P to R, then the tensor product P∗⊗RP can be considered as an R-coalgebra. Furthermore, P and P∗ is a comodule over coalgebra P∗⊗RP. Using the Morita context, this paper give sufficient conditions of clean coalgebra P∗⊗RP and clean P∗⊗RP-comodule P and P∗. These sufficient conditions are determined by the conditions of module P and ring R.

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