| Texto completo | |
| Autor(es): |
Tran Giang Nam
;
Zumbraegel, Jens
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Journal of Pure and Applied Algebra; v. 225, n. 4, p. 22-pg., 2021-04-01. |
| Resumo | |
We investigate the algebra of a Hausdorff ample groupoid, introduced by Steinberg, over a commutative semiring S. In particular, we obtain a complete characterization of congruence-simpleness for such Steinberg algebras, extending the well-known characterizations when S is a field or a commutative ring. We also provide a criterion for the Steinberg algebra A(S)(G(E)) of the graph groupoid G(E) associated to an arbitrary graph E to be congruence-simple. Motivated by a result of Clark and Sims, we show that the natural homomorphism from the Leavitt path algebra L-B(E) to the Steinberg algebra A(B)(G(E)), where B is the Boolean semifield, is an isomorphism if and only if E is row-finite. Moreover, we establish the Reduction Theorem and Uniqueness Theorems for Leavitt path algebras of row-finite graphs over the Boolean semifield B. (C) 2020 Elsevier B.V. All rights reserved. (AU) | |
| Processo FAPESP: | 18/06538-6 - Álgebras de Leavitt de caminhos, álgebras de Steinberg e ações parciais. |
| Beneficiário: | Tran Giang Nam |
| Modalidade de apoio: | Bolsas no Brasil - Pós-Doutorado |