斜多项式环：Schreier技术

IF 0.3 Q4 MATHEMATICS

Acta Mathematica Vietnamica Pub Date : 2022-01-22 DOI:10.1007/s40306-021-00466-7

Phạm Ngọc Ánh

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引用次数: 0

摘要

引入并使用Schreier基证明了斜多项式环是自由理想环，即其单边理想没有唯一秩的环，以及计算单边理想的秩和相应基的描述。后一个事实，即所谓的Schreier-Lewin公式（Lewin Trans.Am.Math.Soc.14455–465 1969），是确定完美局部化的模类型的基本工具，它揭示了经典莱维特代数、偏斜多项式环和自由结合代数之间的紧密联系。

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Skew Polynomial Rings: the Schreier Technique

Schreier bases are introduced and used to show that skew polynomial rings are free ideal rings, i.e., rings whose one-sided ideals are free of unique rank, as well as to compute a rank of one-sided ideals together with a description of corresponding bases. The latter fact, a so-called Schreier-Lewin formula (Lewin Trans. Am. Math. Soc. 145, 455–465 1969), is a basic tool determining a module type of perfect localizations which reveal a close connection between classical Leavitt algebras, skew polynomial rings, and free associative algebras.

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来源期刊

Acta Mathematica Vietnamica MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

期刊介绍： Acta Mathematica Vietnamica is a peer-reviewed mathematical journal. The journal publishes original papers of high quality in all branches of Mathematics with strong focus on Algebraic Geometry and Commutative Algebra, Algebraic Topology, Complex Analysis, Dynamical Systems, Optimization and Partial Differential Equations.