Hotzel asks this for semigroups and right congruences; his and the above version are equivalent. Left congruences on M are equivalence relations closed under all left translations; these are thus equivalent to congruences on the free left M -set on one generator. When M is a group, any left congruence is the decomposition of M into the left cosets of some subgroup, so the lattice of left congru...

In this paper we extend the method of canonical form for congruence bilinear forms to give classification some subclasses 7-dimensional nilpotent Leibniz algebras. Odd-nilpotent algebras are defined as that its even dimensional ideals in lower central series all zero and complex odd-nilpotent with one Leib ideal is obtained by applying aforementioned method.

In this paper, we study fuzzy congruence relations and kernel ideals of an Ockham algebra A , f , whose truth values are in a complete lattice satisfying the infinite meet distributive law. Some equivalent conditions derived for ideal...

This is the latest part of an ongoing project aimed at extending algebraic properties of the classical modular group SL2(Z) to equivalent groups in the theory of Drinfeld modules. We are especially interested in those properties which are important in the classical theory of modular forms. Our results are intended to be applicable to the theory of Drinfeld modular curves and forms. Here we are ...

In the dual-process models of Rothbaum, Weisz, and Snyder (1982) and Heckhausen and Schulz (1995), the self-regulatory capacity to alternate between attempts to directly change (primary control) and psychologically adjust to one’s environment (secondary control) in congruence with performance represents one of its most important yet unexplored theoretical tenets. The present longitudinal study ...

We call a semigroup compactification T of a (discrete) semigroup S Boolean if the underlying space of T is zero-dimensional. The class of Boolean compactifications of S is a complete lattice, in a natural way. Motivated by Numakura’s theoerem, we prove that this lattice is isomorphic to the ideal lattice of the lattice of finite congruence relations of S. We describe in some detail the lattice ...

Forty-three medical students and 78 nursing students each filled out four copies of the Interpersonal Check List. The subjects described self, ideal self as physician or nurse, and typical and ideal work partner. For each questionnaire the two summary scores Dom and Lov were computed. The results indicate a discrepancy between concepts of self and ideal self and the results also point to consid...

We prove that there is a correspondence between self-similar group actions and the class of left cancellative right hereditary monoids satisfying the dedekind height property. The monoids in question turn out to be coextensive with the Zappa-Szép products of free monoids and groups, and the ideal structure of the monoid reflects properties of the group action. These monoids can also be viewed a...

We prove a commutative algebra result which has consequences for congruences between automorphic forms modulo prime powers. If C denotes the congruence module for a fixed automorphic Hecke eigenform π0 we prove an exact relation between the p-adic valuation of the order of C and the sum of the exponents of p-power congruences between the Hecke eigenvalues of π0 and other automorphic forms. We a...