hence it yields an isomorphism between the quotient additive group C/2πiZ and the multiplicative group C×. The group C× is the group of complex points of the multiplicative group Gm; z 7→ e is the exponential function of the multiplicative group Gm. We shall replace this algebraic group by an elliptic curve. We could replace it also by other commutative algebraic groups. As a first example, the...

‎We extend the notion of approximately multiplicative to approximately n-multiplicative maps between locally multiplicatively convex algebras and study some properties of these maps‎. ‎‎W‎e prove that every approximately n-multiplicative linear functional on a functionally continuous locally multiplicatively convex algebra is continuous‎. ‎We also study the relationship between approximately mu...

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For any positive integer n, we call an arithmetical function f(n) as the F.Smarandache multiplicative function if f(1) = 1, and if n > 1, n = p1 1 p α2 2 · · · pk k be the fractorization of n into prime powers, then f(n) = max 1≤i≤k {f(pi i )}. For example, the function S(n) = min{m : m ∈ N, n|m!} is a F.Smarandache multiplicative function. From the definition of S(n), it is easy to see that if...

A condition is identified which guarantees that the coinvariants of a coaction of a Hopf algebra on an algebra form a subalgebra, even though the coaction may fail to be an algebra homomorphism. A Hilbert Theorem (finite generation of the subalgebra of coinvariants) is obtained for such coactions of a cosemisimple Hopf algebra. This is applied for two coactions α, β : A → A⊗O, where A is the co...

We construct multiplicative Green?s (or +Green?s) function for *Sturm-Liouville (*SL) equation. The basic properties of *Green?s are given. Then, *SL equation is evaluated by using function. Effectiveness in *case will thus be seen some examples.

There are several kinds of hyperrings, for example, Krasnerhyperrings, multiplicative hyperring, general hyperrings and$H_v$-rings. In a multiplicative hyperring, the multiplication isa hyperoperation, while the addition is a binary operation. In this paper, the notion of derivation on multiplicative hyperrings is introduced and some related properties are investigated. {bf Keywords:} multiplic...

A binary moment diagram, which was proposed for arithmetic circuit verification, is a directed acyclic graph representing a function from binary-vectors to integers (f : {0, 1}n → Z). A multiplicative binary moment diagram is an extension of a binary moment diagram with edge weights attached. A multiplicative binary moment diagram can represent addition, multiplication and many other functions ...