Module types of localizations, with applcations to Leavitt path algebras

Pham Ngoc, Anh and Siddoway, M. F. (2024) Module types of localizations, with applcations to Leavitt path algebras. ISRAEL JOURNAL OF MATHEMATICS. ISSN 0021-2172

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Abstract

A method of Rosenmann and Rosset for computing module type of fc-localization of free algebras is used to determine module type of quotient rings of free algebras. The now widely studied classical Leavitt algebra LK (1, n) over a field K is seen to be a ring of right quotients of the unital free associative algebra of rank n with respect to the perfect Gabriel ideal topology of a 1-codimensional ideal, i.e., by a nonunital free associative algebra, providing a conceptual, variable- free description of LK (1, n). This result puts Leavitt (path) algebras on the frontier of important research areas in localization theory, quiver algebras, graph operator algebras, and in the study of free ideal rings and their automorphism groups.

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