We solve the matrix equation XA+AX = 0, where A ∈ C is an arbitrary given square matrix, and we compute the dimension of its solution space. This dimension coincides with the codimension of the tangent space of the congruence orbit of A. Hence, we also obtain the (real) dimension of congruence orbits in C. As an application, we determine the generic canonical structure for congruence in C and a...

We prove that monoids Mon〈a, b, c, d : ab = 0, ac = 1, db = 1, dc = 1 dab = 1, dab = 1, . . . , dab = 1〉 are congruence-free for all n ≥ 1. This provides a new countable family of finitely presented congruence-free monoids, bringing one step closer to understanding the Boone–Higman Conjecture. We also provide examples which show that finitely presented congruence-free monoids may have quadratic...

We derive a Mal'cev condition for congruence meet-semidistributivity and then use it to prove two theorems. Theorem A: if a variety in a nite language is congruence meet-semidistributive and residually less than some nite cardinal, then it is nitely based. Theorem B: there is an algorithm which, given m < ! and a nite algebra in a nite language, determines whether the variety generated by the a...

Beta-binders is a recent process calculus developed for modelling and simulating biological systems. As usual for process calculi, the semantic definition heavily relies on a structural congruence. The treatment of the structural congruence is essential for implementation. We present a subset of the calculus for which the structural congruence is decidable and a subset for which it is also effi...

where u and v denote the parameters determining the curves and t is the parameter which determines the points on the curve. By this method of definition the equations of a congruence of curves are given a form similar to that usually adopted in the discussions of rectilinear congruences, so that one proceeds naturally to a generalization of some of the properties of the latter. At the same time...

For an arbitrary algebra A a new labelling, called the signed labelling, of the Hasse diagram of Con A is described. Under the signed labelling, each edge of the Hasse diagram of Con A receives a label from the set {+,−}. The signed labelling depends completely on a subset of the unary polynomials of A and its inspiration comes from semigroup theory. For finite algebras, the signed labelling co...

We establish a direct correspondence between two congruence properties for finite algebras. The first property is that minimal sets of type i omit tails. The second property is that congruence lattices omit pentagons of type i.

The current research challenges the widespread truism that recalling a positive self necessarily increases self-esteem, whereas recalling a negative self necessarily decreases self-esteem. Four experiments demonstrate that chronically happy people show a relative increase in self-esteem by recalling either a positive or a negative self. Chronically sad people, however, show a relative decrease ...

The aim of this study is to test the “work values” inventory developed by Tevruz and Turgut and to utilize the concept in a model, which aims to create a greater understanding of the work experience. In the study multiple effects of work values, work-value congruence and work centrality on organizational citizenship behavior are examined. In this respect, it is hypothesized that work values and...

We construct a diagram D⊲⊳, indexed by a finite partially ordered set, of finite Boolean 〈∨, 0, 1〉-semilattices and 〈∨, 0, 1〉-embeddings, with top semilattice 2, such that for any variety V of algebras, if D⊲⊳ has a lifting, with respect to the congruence lattice functor, by algebras and homomorphisms in V, then there exists an algebra U in V such that the congruence lattice of U contains, as a...