منابع مشابه
Lattice Homomorphisms Induced by Group Homomorphisms
Introduction. By a lattice homorphism of a group G onto a group G' we mean a single-valued mapping of the lattice L(G) of subgroups of G onto the lattice L(G') of subgroups of G', which preserves all unions and intersections, that is, which is subject to the conditions 1. (U,S,)0 = U,(S¿), 2. (r\vSr) = Ç)ASd>), for every (finite or infinite) set of subgroups 5„ of G. We call proper any l...
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We decompose a matrix Y into a sum of rank one bilinear forms in a stepwise manner, by considering Y as a mapping from the finite dimensional space l r to the space l p . We provide transition formulas, and represent them in a duality diagram, thus generalizing the well known duality diagram in the french school of data analysis. As an application, we introduce a family of Euclidean multidimens...
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Using the fixed point method, we prove the Hyers–Ulam stability of the Cauchy–Jensen functional equation and of the Cauchy–Jensen functional inequality in fuzzy Banach ∗-algebras and in induced fuzzy C-algebras. Furthermore, using the fixed point method, we prove the Hyers–Ulam stability of fuzzy ∗-derivations in fuzzy Banach ∗-algebras and in induced fuzzy C-algebras. Published by Elsevier Ltd
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If (G, *) and (H, •) are groups, then a function f : G −→ H is a homomorphism if f (x * y) = f (x) • f (y) for all x, y ∈ G. Example: Let (G, *) be an arbitrary group and H = {e}, then the function f : G −→ H such that f (x) = e for any x ∈ G is a homomorphism. In fact, f (x * y) = e = e • e = f (x) • f (y). f (x) = x for any x ∈ G is a homomorphism. In fact, f (x * y) = x * y = f (x) * f (y). ...
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We present here new hierarchies of literal varieties of languages. Each language under consideration is a disjoint union of a certain collection of “basic” languages described here. Our classes of languages correspond to certain literal varieties of homomorphisms from free monoids onto nilpotent groups of class ≤ 2.
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1969
ISSN: 0001-8708
DOI: 10.1016/0001-8708(69)90003-6