منابع مشابه
On a Special Congruence of Carlitz
We prove that if q is a power of a prime p and p divides a, with k ≥ 0, then 1 + (q − 1) ∑ 0≤b(q−1)<a ( a b(q − 1) ) ≡ 0 (mod p). The special case of this congruence where q = p was proved by Carlitz in 1953 by means of rather deep properties of the Bernoulli numbers. A more direct approach produces our generalization and several related results.
متن کاملSpecial Congruence Triples for a Regular Semigroup
With the usual notation for congruences on a regular semigroup S, in a previous communication we studied the lattice Λ generated by Γ = {σ, τ, μ, β} relative to properties such as distributivity and similar conditions. For K and T the kernel and trace relations on the congruence lattice of S, we form an abstraction of the triple (Λ;K|Λ, TΛ) called a c-triple. In this study a number of relations...
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We study the problem of representing a pair of algebraic lattices, L1 and L0, as Con(A1) and Con(A0), respectively, with A1 an algebra and A0 a subalgebra of A1, and we provide such a representation in a special case. Back in 1971, Ervin Fried posed the problem of representing a pair of algebraic lattices, L1 and L0, as Con(A1) and Con(A0), respectively, with A1 an algebra and A0 a subalgebra o...
متن کاملA Special Congruence Lattice of a Regular Semigroup
Let S be a regular semigroup and C its lattice of congruences. We consider the sublattice Λ of C generated by σ-the least group, τ -the greatest idempotent pure, μ-the greatest idempotent separating and β-the least band congruence on S. To this end, we study the following special cases: (1) any three of these congruences generate a distributive lattice, (2) Λ is distributive, (3) the restrictio...
متن کاملCongruence between parents' and adolescents' reports of special health care needs in a Title XXI program.
OBJECTIVES The purpose of this study was to examine agreement between adolescents and their parents about whether or not the adolescent had a special health care need, using the Children with Special Health Care Needs (CSHCN) Screener. METHODS Telephone surveys that included the CSHCN Screener were conducted with 522 adolescents and their parents who were new enrollees in Florida's State Chil...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1953
ISSN: 0002-9939
DOI: 10.2307/2031833