Geodesic
On linear operators strongly preserving invariants of Boolean matrices
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 1, pp. 169-186

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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.
DOI : 10.1007/s10587-012-0004-y
Classification : 06E05, 15A04, 15A09, 15A86, 15B34, 16Y60
Keywords: linear operator; invariant; regular matrix; invertible matrix; general Boolean algebra 
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Chen, Yizhi; Zhao, Xianzhong. On linear operators strongly preserving invariants of Boolean matrices. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 1, pp. 169-186. doi: 10.1007/s10587-012-0004-y

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