-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 functions on smalgebras
Malcev sequences and associative symmetrisations.
Mal'cev type conditions for two varieties
Mal'cev-type theorems for partial congruences
Mal'tsev--Neumann products of semi-simple classes of rings
Malt’tsev–Neumann products of semi-simple classes of associative rings are studied and some conditions which ensure that such a product is again a semi-simple class are obtained. It is shown that both products, and of semi-simple classes and are semi-simple classes if and only if they are equal.
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...
Maximal submonoids of monoids of hypersubstitutions
For a monoid M of hypersubstitutions, the collection of all M-solid varieties forms a complete sublattice of the lattice L(τ) of all varieties of a given type τ. Therefore, by the study of monoids of hypersubstitutions one can get more insight into the structure of the lattice L(τ). In particular, monoids of hypersubstitutions were studied in [9] as well as in [5]. We will give a complete characterization of all maximal submonoids of the monoid Reg(n) of all regular hypersubstitutions of type τ...
Medial groupoids and Mersenne numbers
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