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On linear operators strongly preserving invariants of Boolean matrices

Yizhi Chen, Xian Zhong Zhao (2012)

Czechoslovak Mathematical Journal

Let 𝔹 k be the general Boolean algebra and T a linear operator on M m , n ( 𝔹 k ) . If for any A in M m , n ( 𝔹 k ) ( M n ( 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 𝔹 k . Meanwhile, noting that a general Boolean algebra 𝔹 k is isomorphic...

On locales whose countably compact sublocales have compact closure

Themba Dube (2023)

Mathematica Bohemica

Among completely regular locales, we characterize those that have the feature described in the title. They are, of course, localic analogues of what are called cl -isocompact spaces. They have been considered in T. Dube, I. Naidoo, C. N. Ncube (2014), so here we give new characterizations that do not appear in this reference.

On Marczewski-Burstin representable algebras

Marek Balcerzak, Artur Bartoszewicz, Piotr Koszmider (2004)

Colloquium Mathematicae

We construct algebras of sets which are not MB-representable. The existence of such algebras was previously known under additional set-theoretic assumptions. On the other hand, we prove that every Boolean algebra is isomorphic to an MB-representable algebra of sets.

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