Tiled orders, exponent matrixes, units in rings and related topics
| Full text | |
| Author(s): |
Dokuchaev, Mikhailo
;
Kirichenko, Vladimir
;
Kudryavtseva, Ganna
;
Plakhotnyk, Makar
Total Authors: 4
|
| Document type: | Journal article |
| Source: | Journal of Algebra; v. 490, p. 1-20, NOV 15 2017. |
| Web of Science Citations: | 0 |
| Abstract | |
An exponent matrix is an n x n matrix A = (a(ij)) over N-0 satisfying (1) a(ii) = 0 for all i = 1, ... , n and (2) a(ij) + a(jk) >= a(ik) for all pairwise distinct i, j, k is an element of[1, ... , n]. In the present paper we study the set epsilon(n) of all non-negative n x n exponent matrices as an algebra with the operations circle plus of component-wise maximum and circle dot of component-wise addition. We provide a basis of the algebra (epsilon(n), circle plus, circle dot, 0) and give a row and a column decompositions of a matrix A is an element of epsilon(n) with respect to this basis. This structure result determines all n x n-tiled orders over a fixed discrete valuation domain. We also study automorphisms of epsilon(n) with respect to each of the operations circle plus and circle dot and prove that Aut(epsilon(n), circle plus, circle dot, 0) congruent to Aut(epsilon(n), circle plus) congruent to Aut(epsilon(n), circle dot) congruent to S-n X C-2, n > 2. (C) 2017 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 15/09162-9 - Non commutative algebra and applications |
| Grantee: | Francisco Cesar Polcino Milies |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 13/11350-2 - Tiled orders, partial actions and homological aspects |
| Grantee: | Makar Plakhotnyk |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 15/16726-6 - Tiled orders, exponent matrixes, units in rings and related topics |
| Grantee: | Mikhailo Dokuchaev |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |
| FAPESP's process: | 14/23853-1 - Partial actions, restriction semigroups and operator algebras |
| Grantee: | Mikhailo Dokuchaev |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |