For a pseudo $MV$-algebra $\mathcal A$ we denote by $\ell (\mathcal A)$ the underlying lattice of $\mathcal A$. In the present paper we investigate the algebraic properties of maximal convex chains in $\ell (\mathcal A)$ containing the element 0. We generalize a result of Dvurečenskij and Pulmannová.
The set of all $m\times n$ Boolean matrices is denoted by ${\mathbb M}_{m,n}$. We call a matrix $A\in {\mathbb M}_{m,n}$ regular if there is a matrix $G\in {\mathbb M}_{n,m}$ such that $AGA=A$. In this paper, we study the problem of characterizing linear operators on ${\mathbb M}_{m,n}$ that strongly preserve regular matrices. Consequently, we obtain that if $\min \{m,n\}\le 2$, then all operators on ${\mathbb M}_{m,n}$ strongly preserve regular matrices, and if $\min \{m,n\}\ge 3$, then an operator $T$ on ${\mathbb M}_{m,n}$ strongly preserves regular matrices if and only if there are invertible matrices $U$ and $V$ such that $T(X)=UXV$ for all $X\in {\mathbb M}_{m,n}$, or $m=n$ and $T(X)=UX^TV$ for all $X\in {\mathbb M}_{n}$.
In 2019, a metal-detector find of an exceptionally well-preserved weapon was made in the complex of Ždánice Forest. We can classify it as a long-sword of Type XVIa, H1, 1b (according to Oakeshott 1964; Głosek 1984, 39–40, Fig. 4) and date it to the turn of the 15th century. Its blade was marked on both sides with three marks taking the form of a forked cross, a diagonal consisting of three equilateral crosses and, finally, a bishop's crosier. The weapon was assembled from a blade of Passau provenance and hilt-components characteristic of the wider Central European region. These and other facts concerning the sword were obtained through detailed analysis, which this study introduces.