Algebra

1907 Submissions

[5] viXra:1907.0443 [pdf] submitted on 2019-07-23 14:38:41

Compound Numbers with Dimension 5, 6 and 7

Authors: Valery Timin
Comments: language: Russian, number of pages: 6, mailto:timinva@yandex.ru, Creative Commons Attribution 3.0 License

This work is devoted to the search, study and compilation of the multiplication table of a composite hyperbolic (Hypercomplex) number of dimension five, six, seven (5,6,7): q = {1, i, j, k, l}: i2 = 1, j2 = 1, k2 = 1, l2 = 1. On this basis, as a template, you can pick up other multiplication tables with a different target or arbitrary arrangement of plus (+) and minus (-) signs in the cells of the multiplication table. The disadvantage of this multiplication table is its weak associativity and not commutativity (not even anti-commutativity). But this is its fundamental property. Эта работа посвящена поиску, изучению и составлению таблицы умножения составного гиперболического (гиперкомплексного) числа размерностью пять, шесть и семь (5,6,7):
Category: Algebra

[4] viXra:1907.0395 [pdf] submitted on 2019-07-20 09:15:19

Compound Numbers with Dimension 5

Authors: Valery Timin
Comments: language: Russian, number of pages: 4, mailto:timinva@yandex.ru, Creative Commons Attribution 3.0 License

This work is devoted to the search, study and compilation of the multiplication table of a composite hyperbolic (Hypercomplex) number of dimension five (5): q = {1, i, j, k, l}: i2 = 1, j2 = 1, k2 = 1, l2 = 1. On this basis, as a template, you can pick up other multiplication tables with a different target or arbitrary arrangement of plus (+) and minus (-) signs in the cells of the multiplication table. The disadvantage of this multiplication table is its weak associativity and not commutativity (not even anti-commutativity). But this is its fundamental property. Эта работа посвящена поиску, изучению и составлению таблицы умножения составного гиперболического (гиперкомплексного) числа размерностью пять (5).
Category: Algebra

[3] viXra:1907.0332 [pdf] submitted on 2019-07-18 01:16:19

Sketches On Polysigns And Other Arithmetics Operators

Authors: Kujonai
Comments: 48 Pages.

A compilation of drawings sprung during a email exchanging with T. Golden, author of the Polysigns numbers. It must be mentioned that he accepts only some of the concepts presented here. Although we do share some common ground while talking about Polysigns and/or "simplexogonal" arithmetics, we do have some differences in the approach. In anycase, it is required some understanding of the Polysign Notation to fully appreciate the drawings. A few important bits arose as a direct consequence of the interaction and some are presented here, in a rather highly informal way.
Category: Algebra

[2] viXra:1907.0162 [pdf] replaced on 2019-07-21 05:56:55

Solutions to Problems in Topics in Algebra

Authors: Henry Wong
Comments: 1 Page.

An addendum to group theory.
Category: Algebra

[1] viXra:1907.0117 [pdf] submitted on 2019-07-07 10:09:59

The $\phi$-Derivations

Authors: Antoine Balan
Comments: 1 page, written in english

We propose a generalization of the derivations with help of homomorphism.
Category: Algebra