The abstract decryption structure can be used to analyze what decryption structure with respect to the resulting ciphertext would result in additive and multiplicative homomorphism
Using the facts that [[kappa].sub.I] and [psi] are algebra homomorphisms
and that [t.sub.i,j,l] = [sigma]([t.sub.i,j,l]), where
Let [sigma], [tau]: M [right arrow] M be continuous homomorphisms
with the condition [[sigma].sup.2] = [sigma] and [[tau].sup.2] = [tau].
Let [G.sub.1] and [G.sub.2] be two graphs; then there is a homomorphism
f: [G.sub.1] [right arrow] [G.sub.2] iff [G.sub.2] is a retract of [G.sub.1][bar.V][G.sub.2].
The endomorphism algebra [End.sub.k](M, [mu]) can be considered as a monoidal Hom-algebra, where the Hom-multiplication is the composite of morphisms, the unit is the identity homomorphism
, and the twisting map [iota]: [End.sub.k](M, [mu]) [right arrow] [End.sub.k](M, [mu]) is given by [iota]([phi]) = [mu][phi][[mu].sup.-1], for [phi] [member of] [End.sub.k](M, [mu]).
We remark also that the pair of homomorphisms
([tau][beta][phi]', [psi]') are the homomorphisms
induced by ([bar.[beta]] [bar.f], [bar.g]) by fixing the lifts ([beta][~.f], [~.g]).
Let f : M [right arrow] N be a BCK-module homomorphism
and let [PHI] [member of] BF(M) be a bipolar fuzzy set on M.
Kaboli Gharetapeh, "Approximately n-Jordan homomorphisms
on Banach algebras," Journal of Inequalities and Applications, vol.
(a) when L is of the form pV(K) for some rational subset K of [X.sup.+], where pV is the natural continuous homomorphism
from [[??].sub.X]S to [[??].sub.X]V;
This is analogous to the definition of fractional chromatic number by means of homomorphisms
to Kneser graphs (or of circular chromatic number by circulants).