| Title:
|
On linear operators strongly preserving invariants of Boolean matrices (English) |
| Author:
|
Chen, Yizhi |
| Author:
|
Zhao, Xianzhong |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
|
169-186 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\mathbb {B}_{k}$ be the general Boolean algebra and $T$ a linear operator on $M_{m,n}(\mathbb {B}_{k})$. If for any $A$ in $M_{m,n}(\mathbb {B}_{k})$ ($ M_{n}(\mathbb {B}_{k})$, respectively), $A$ is regular (invertible, respectively) if and only if $T(A)$ is regular (invertible, respectively), then $T$ is said to strongly preserve regular (invertible, respectively) matrices. In this paper, we will give complete characterizations of the linear operators that strongly preserve regular (invertible, respectively) matrices over $\mathbb {B}_{k}$. Meanwhile, noting that a general Boolean algebra $\mathbb {B}_{k}$ is isomorphic to a finite direct product of binary Boolean algebras, we also give some characterizations of linear operators that strongly preserve regular (invertible, respectively) matrices over $\mathbb {B}_{k}$ from another point of view. (English) |
| Keyword:
|
linear operator |
| Keyword:
|
invariant |
| Keyword:
|
regular matrix |
| Keyword:
|
invertible matrix |
| Keyword:
|
general Boolean algebra |
| MSC:
|
06E05 |
| MSC:
|
15A04 |
| MSC:
|
15A09 |
| MSC:
|
15A86 |
| MSC:
|
15B34 |
| MSC:
|
16Y60 |
| idZBL:
|
Zbl 1249.15034 |
| idMR:
|
MR2899743 |
| DOI:
|
10.1007/s10587-012-0004-y |
| . |
| Date available:
|
2012-03-05T07:22:06Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142049 |
| . |
| Reference:
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