相关论文: On tolerances representable as $R \circ R^-$

We discuss two possible ways of representing tolerances: first, as a homomorphic image of some congruence; second, as the relational composition of some compatible relation with its converse. The second way is independent from the variety…

We introduce the notion of a nest-representable tolerance and show that some results from our former paper "From congruence identities to tolerance identities" [CT] can be extended to this more general setting.

An identity s=t is linear if each variable occurs at most once in each of the terms s and t. Let T be a tolerance relation of an algebra A in a variety defined by a set of linear identities. We prove that there exist an algebra B in the…

We prove that a tolerance relation of a lattice is a homomorphic image of a congruence relation.

This paper aims at the following results: \begin{enumerate} \item The class of all $*$-regular rings forms a variety. \item A subdirectly irreducible $*$-regular ring $R$ is faithfully representable (i.e. isomorphic to a subring of an…

We define reflective numbers and their iterative summations. We provide classification of reflective numbers based on their iterative cyclical limits.

The homomorphic image of a congruence is always a tolerance (relation) but, within a given variety, a tolerance is not necessarily obtained this way. By a Maltsev-like condition, we characterize varieties whose tolerances are homomorphic…

We show that a variety $\mathcal V$ is congruence distributive if and only if there is some $h$ such that the inclusion (1) $\Theta \cap ( \sigma \circ \sigma ) \subseteq ( \Theta \cap \sigma ) \circ ( \Theta \cap \sigma ) \circ \dots $…

If $A$ is an algebra and \bgt is a tolerance on $A$, then $A/\bgt$ is a multi-algebra in a natural way. We give an example to show that not every multi-algebra arises in this manner. We slightly generalize the construction of $A/\bgt$ and…

We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.

We present some identities dealing with reflexive and admissible relations and which, through a variety, are equivalent to congruence modularity.

This communication records some observations made in the course of studying one-relator groups from the point of view of residual solvability. As a contribution to clas- sification efforts we single out some relator types that render the…

We introduce a model to design reflectors that take into account the inverse square law for radiation. We prove existence of solutions, both in the near and far field cases, when the input and output energies are prescribed.

In a general algebraic setting, we state some properties of commutators of reflexive admissible relations.

A general procedure is presented to determine, given any suitable representation of the modular group, the characters of all possible Rational Conformal Field Theories whose associated modular representation is the given one. The relevant…

In part I we introduced the class ${\mathcal E}_2$ of Lie subgroups of $Sp(2,\R)$ and obtained a classification up to conjugation (Theorem 1.1). Here, we determine for which of these groups the restriction of the metaplectic representation…

We calculate extensions between certain irreducible admissible representations of p-adic groups.

We shall consider nonrestricted representations of $C_l-$ type Lie algebra over an algebraically closed field of characteristic $p\geq7.$ This paper gives some counter examples to important theory relating to the representations of modular…

This paper provides a general characterization of preferences that admit a Richter-Peleg representation without imposing completeness or transitivity. We establish that a binary relation on a nonempty set admits a Richter-Peleg…

In this paper, we fully characterize maximal representations of a C*-correspondence. This strengthens several earlier results. We demonstrate the criterion with diverse examples. We also describe the noncommutative Choquet boundary and…