Algebra

1906 Submissions

 viXra:1906.0485 [pdf] submitted on 2019-06-25 08:38:38

On the Equation 2*cosh(2x)*(tanh(exp(-X)))*(tanh(exp(-X)))-1=0

Authors: Edgar Valdebenito

We give a formula for Pi.
Category: Algebra

 viXra:1906.0475 [pdf] submitted on 2019-06-26 01:58:32

Form Invariant High Order Differentials

Authors: Han Xiao

Traditionally, an infinitesimal is regarded as a variable that runs toward 0. Since a differential is a kind of infinitesimal, a differential is essentially a variable running toward 0 too. As a result, differentials are form invariant but not meaning invariant. This paper proposes a Number Field of Ordered Infinitesimals and Infinities (OII Number Field) which can be seen as a kind of extension of real number field. The terminus of a variable running toward 0 is no longer 0, but a point in the OII Number Field, with an Order and a Weight. In this way, the process of running is recorded in the destination, making infinitesimals a kind of number which can be compared and operated easily. On this basis, the differential of a variable is invariant not only in form, but also in meaning. As a differential becomes a variable on another number axis parallel to the real number axis in OII Number Field, a differential can generate differential too, thus giving rise to high order differentials which are also invariant both in form and in meaning.
Category: Algebra

 viXra:1906.0447 [pdf] replaced on 2019-06-25 14:27:50

Study of (σ,τ)-Generalized Derivations with Their Composition of Semiprime Rings

Authors: Ajda Foˇsner, Mehsin Jabel Atteya

The main purpose of this paper is to study and investigate certain results concerning the (σ,τ)-generalized derivation D associated with the (σ,τ)-derivation d of semiprime and prime rings R, where σ and τ act as two automorphism mappings of R. We focus on the composition of (σ,τ)-generalized derivations of the Leibniz’s formula, where we introduce the general formula to compute the composition of the (σ,τ)-generalized derivation D of R.
Category: Algebra

 viXra:1906.0343 [pdf] submitted on 2019-06-18 09:09:35

{ e, (1 2)(3 4), (1 3)(2 4), (1 4)(2 3)} is Normal in the Symmetric Group of Degree 4

Authors: Henry Wong

An addendum to group theory.
Category: Algebra

 viXra:1906.0304 [pdf] replaced on 2019-08-17 10:29:26

On Vector Subspaces

Authors: Anamitra Palit

The short writing seeks to demonstrate certain lapses in the theory of the linear vector spaces.
Category: Algebra

 viXra:1906.0145 [pdf] submitted on 2019-06-09 22:32:11

Solutions to Problems in Abstract Algebra

Authors: Henry Wong

An addendum to group theory.
Category: Algebra

 viXra:1906.0120 [pdf] submitted on 2019-06-07 08:34:30

On the Equation 8*x*x*(cos(x))*(cos(x))-(4-2*sqrt(2))*x*x-1=0

Authors: Edgar Valdebenito