Acta Mathematica Vietnamica
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Skew Polynomial Rings: the Schreier Technique
Phạm Ngọc Ánhpp. 5-17
Abstract
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.
Special Issue: Algebra, Geometry and Related Topics