Note that additive homomorphism
is obtained obviously, we thus only focus on how to obtain multiplicative homomorphism
Then the maps [i.sub.A] and [i.sub.C] are continuous algebra homomorphisms
. Moreover, the quotient map [[kappa].sub.I] : T [right arrow] A [??] C is a continuous algebra homomorphism
Let [sigma]: M [right arrow] M be a continuous homomorphism
and d: M [right arrow] M a [sigma]-derivation.
(2) Define a homomorphism
[zeta] : (M [cross product] [M.sup.*], [mu] [cross product] [([[mu].sup.*]).sup.-1] [right arrow] ([End.sub.k](M, [mu]), [iota]) in [??]([M.sub.k]) by
Then there is a homomorphism
[r.sub.1] : [G.sub.1] [right arrow] [K.sub.n] such that [r.sub.1](x) = x, or a homomorphism
[r.sub.2] : [G.sub.2] [right arrow] [K.sub.n] such that [r.sub.2] (x) = x, for any vertex x of [K.sub.n].
A set-valued mapping H : [Q.sub.t] [right arrow] [P.sup.*] ([Q'.sub.t]) is called a strong set-valued homomorphism
if we replace inclusion by equality in (1) and (2).
Image Encryption with Homomorphism
. This component can be divided into two parts: the preprocessed image generation with prediction and homomorphism
where the ring homomorphism
f# : Z[[intersection]] [right arrow] Z [[pi]] is defined by
Let f : R [right arrow] S be a ring homomorphism
. If [xi] is a 2-absorbing primary fuzzy ideal of S, then [f.sup.-1] ([xi]) is a 2absorbing primary fuzzy ideal of R.
A 2-Jordan homomorphism
is called simply a Jordan homomorphism
(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;