| ID | 66004 |
| FullText URL | |
| Author |
Puthenpurakal, Tony J.
Department of Mathematics, IIT Bombay
|
| Abstract | Let (A,m) be an excellent Henselian Cohen-Macaulay local ring of finite representation type. If the AR-quiver of A is known then by a result of Auslander and Reiten one can explicity compute G(A) the Grothendieck group of finitely generated A-modules. If the AR-quiver is not known then in this paper we give estimates of G(A)Q = G(A) ⊗Z Q when k = A/m is perfect. As an application we prove that if A is an excellent equi-characteristic Henselian Gornstein local ring of positive even dimension with char A/m ≠ 2, 3, 5 (and A/m perfect) then G(A)Q ≅ Q.
|
| Keywords | Grothendieck group
finite representation type
AR sequence
|
| Note | Mathematics Subject Classification. Primary 13D15; Secondary 16G50, 16G60, 16G70
|
| Published Date | 2024-01
|
| Publication Title |
Mathematical Journal of Okayama University
|
| Volume | volume66
|
| Issue | issue1
|
| Publisher | Department of Mathematics, Faculty of Science, Okayama University
|
| Start Page | 103
|
| End Page | 113
|
| ISSN | 0030-1566
|
| NCID | AA00723502
|
| Content Type |
Journal Article
|
| language |
English
|
| Copyright Holders | Copyright ©2024 by the Editorial Board of Mathematical Journal of Okayama University
|
| File Version | publisher
|
| Refereed |
True
|
| Submission Path | mjou/vol66/iss1/7
|
