scholarly journals Modules without invariant basis number

1957 ◽  
Vol 8 (2) ◽  
pp. 322-322 ◽  
Author(s):  
W. G. Leavitt
Keyword(s):  
Invariant Basis ◽  
Invariant Basis Number

scholarly journals Cohn–Leavitt path algebras and the invariant basis number property

2019 ◽  
Vol 18 (05) ◽  
pp. 1950086 ◽  
Author(s):  
Müge Kanuni̇ ◽  
Murad Özaydin
Keyword(s):  
Finite Graph ◽  
Path Algebra ◽  
Necessary Condition ◽  
Leavitt Path Algebra ◽  
Morita Equivalent ◽  
Path Algebras ◽  
Invariant Basis ◽  
K Theory ◽  
Leavitt Path Algebras ◽  
Invariant Basis Number

We give the necessary and sufficient condition for a separated Cohn–Leavitt path algebra of a finite digraph to have Invariant Basis Number (IBN). As a consequence, separated Cohn path algebras have IBN. We determine the non-stable K-theory of a corner ring in terms of the non-stable K-theory of the ambient ring. We give a necessary condition for a corner algebra of a separated Cohn–Leavitt path algebra of a finite graph to have IBN. We provide Morita equivalent rings which are non-IBN, but are of different types.

scholarly journals Cohn Path Algebras have Invariant Basis Number

2015 ◽  
Vol 44 (1) ◽  
pp. 371-380 ◽  
Author(s):  
Gene Abrams ◽  
Müge Kanuni
Keyword(s):  
Path Algebras ◽  
Invariant Basis ◽  
Invariant Basis Number

Affine geometry of modules over a ring with invariant basis number

2007 ◽  
Vol 82 (5-6) ◽  
pp. 756-765
Author(s):  
A. A. Lashkhi ◽  
T. G. Kvirikashvili
Keyword(s):  
Affine Geometry ◽  
Invariant Basis ◽  
Invariant Basis Number

scholarly journals A Note on Invariant Basis Number and Types for Strongly Graded Rings

2021 ◽  
Vol 37 (1) ◽  
Author(s):  
Nguyen Quang Loc
Keyword(s):  
Finite Group ◽  
Graded Rings ◽  
Identity Component ◽  
Invariant Basis ◽  
Invariant Basis Number ◽  
Positive Integers

: Given any pair of positive integers (n, k) and any nontrivial finite group G, we show that there exists a ring R of type (n, k) such that R is strongly graded by G and the identity component Re has Invariant Basis Number. Moreover, for another pair of positive integers (n', k') with n ≤ n' and k | k', it is proved that there exists a ring R of type (n, k) such that R is strongly graded by G and Re has type (n', k'). These results were mentioned in [G. Abrams, Invariant basis number and types for strongly graded rings, J. Algebra 237 (2001) 32-37] without proofs.  

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