Abstract
AbstractSchreier 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.
Funder
Nemzeti Kutatási Fejlesztési és Innovációs Hivatal
ELKH Alfréd Rényi Institute of Mathematics
Publisher
Springer Science and Business Media LLC
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