Matrix versions of aperiodic -rational identities
Maximal column rank preservers of fuzzy matrices
This paper concerns two notions of rank of fuzzy matrices: maximal column rank and column rank. We investigate the difference of them. We also characterize the linear operators which preserve the maximal column rank of fuzzy matrices. That is, a linear operator T preserves maximal column rank if and only if it has the form T(X) = UXV with some invertible fuzzy matrices U and V.
Medial modes and rectangular algebras
Medial modes, a natural generalization of normal bands, were investigated by Płonka. Rectangular algebras, a generalization of rectangular bands (diagonal modes) were investigated by Pöschel and Reichel. In this paper we show that each medial mode embeds as a subreduct into a semimodule over a certain ring, and that a similar theorem holds for each Lallement sum of cancellative modes over a medial mode. Similar results are obtained for rectangular algebras. The paper generalizes earlier results...
Monoides de comptage et langages rationnels.
Monoides et semi-anneaux complets.
Monoides et semi-anneaux continus.
Multiplicatively idempotent semirings
Semirings are modifications of unitary rings where the additive reduct does not form a group in general, but only a monoid. We characterize multiplicatively idempotent semirings and Boolean rings as semirings satisfying particular identities. Further, we work with varieties of enriched semirings. We show that the variety of enriched multiplicatively idempotent semirings differs from the join of the variety of enriched unitary Boolean rings and the variety of enriched bounded distributive lattices....