-solid varieties and -free clones
Mal'cev conditions for congruence-regular and congruence-permutable varieties
Mal'cev conditions for directly decomposable compatible relations
Mal'cev-type theorems for partial congruences
Matrices of homomorphic mappings
Maximal clones and maximal permutation groups
A fundamental result in universal algebra is the theorem of Rosenberg describing the maximal subclones in the clone of all operations over a finite set. In group theory, the maximal subgroups of the symmetric groups are classified by the O'Nan-Scott Theorem. We shall explore the similarities and differences between these two analogous major results. In addition, we show that a primitive permutation group of diagonal type can be maximal in the symmetric group only if its socle is the direct product...
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.
Maximal Primal Clusters Are Infinite.
Maximal solutions of two–sided linear systems in max–min algebra
Max-min algebra and its various aspects have been intensively studied by many authors [1, 4] because of its applicability to various areas, such as fuzzy system, knowledge management and others. Binary operations of addition and multiplication of real numbers used in classical linear algebra are replaced in max-min algebra by operations of maximum and minimum. We consider two-sided systems of max-min linear equations , with given coefficient matrices and . We present a polynomial method for...
Medial idempotent groupoids. I
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...
Median groups
Meet-preserving free functors
Metrics and tolerances
Minimal algebras and category equivalences
Minimal algebras in some class of algebras
Minimal compatible tolerances on lattices
Minimal conditions on Clifford semigroup congruences.
Minimal generics from subvarieties of the clone extension of the variety of Boolean algebras
Let τ be a type of algebras without nullary fundamental operation symbols. We call an identity φ ≈ ψ of type τ clone compatible if φ and ψ are the same variable or the sets of fundamental operation symbols in φ and ψ are nonempty and identical. For a variety of type τ we denote by the variety of type τ defined by all clone compatible identities from Id(). We call the clone extension of . In this paper we describe algebras and minimal generics of all subvarieties of , where is the variety of...
Mittelwertstrukturen.