Draft:Unbounded generating number
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Comment: cite to secondary sources to demonstrate WP:Notability microbiologyMarcus (petri dish·growths) 20:33, 29 December 2023 (UTC)
See rank condition
In mathematics, more specifically in the field of ring theory, a ring R has unbounded generating number (UGN) if, for each positive integer m, any set of generators for the free right R-module Rm has cardinality ≥m.[1]
Rings with unbounded generating number have in the literature also been referred to as satisfying the rank condition.[2]
The definition is left–right symmetric, so it makes no difference whether we define UGN in terms of left or right modules; the two definitions are equivalent.[3]
References
Sources
- Abrams, Gene; Nam, Tran Giang; Phuc, Ngo Tan (2017), "Leavitt path algebras having unbounded generating number", J. Pure Appl. Algebra, 221 (6): 1322–1343, arXiv:1603.09695, doi:10.1016/j.jpaa.2016.09.014, ISSN 1873-1376, MR 3599434
- Lam, Tsit Yuen (1999), Lectures on modules and rings, Graduate Texts in Mathematics, vol. 189, New York: Springer-Verlag, pp. xxiv+557, ISBN 0-387-98428-3, MR 1653294