Algebra

Previous months:
2026 - 2601(1) - 2603(1) - 2607(1)

Recent submissions

Any replacements are listed farther down

[3] ai.viXra.org:2607.0051 [pdf] submitted on 2026-07-21 17:44:48

The Trinions: The Natural Extension of the Complex and Dual Numbers

Authors: Joerg Moesch
Comments: 27 Pages.

In this paper, the natural three-dimensional extension of the complex and dual numbers is introduced: the trinion algebras Y(k) of the form a+bi+cj with i²=-1, j²=0 and the commutative coupling ij=ji=k, where k = α+βi+γj is an element of the algebra. The family Y(k) is systematically investigated: multiplication, division and inverses are derived. Special attention is given to the phenomena induced by non-associativity, which lead to invertible zero divisors, non-unique division, and rich geometric structures. The eight fundamental algebras with α,β,γ ∈ {0,1} are examined and their zero divisor sets are visualized. Numerical examples for the algebra Y(1) illustrate the observed phenomena.
Category: Algebra

[2] ai.viXra.org:2603.0055 [pdf] submitted on 2026-03-12 18:00:46

Toward an Algebraic Revolution: Analytical Resolution of the Quintic Through Quartic Reduction and Universal Scaling Law

Authors: Ahcene Ait Saadi
Comments: 6 Pages.

This paper presents an original analytical method for solving the reduced quintic equation By establishing a conformal mapping between the roots of an auxiliary quartic and those of the quintic, we reveal a Universal Scaling Law governed by a 1/8 power factor. This approach calculates all five roots (real and complex) across all topological regimes, including cases with three real roots, with a precision of . This discovery marks a new era for polynomial algebra.
Category: Algebra

[1] ai.viXra.org:2601.0030 [pdf] submitted on 2026-01-10 01:38:08

An Elementary Proof os Feramt´s Last Theorem .a Complete Proorf for All Powers N>3

Authors: Eero Koskela
Comments: 10 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)

We present an elementary proof of Fermat's Last Theorem for all powers n ≥ 3 using only binomial coefficients and basic algebra. The proof establishes that the binomial representation 6C(x+1,3) + x serves as a unique fingerprint for the cube x³, and demonstrates that this uniqueness property forces a secondary constraint that is incompatible with the original Fermat equation. For n=3, this leads directly to a geometric contradiction. For n=4, we obtain an algebraic impossibility. For n ≥ 5, we show that the secondary constraint forces fractional exponents that can only yield integers if a lower-dimensional Fermat equation holds—but these are already proven impossible. This proof is independent of Wiles's work and relies only on elementary techniques accessible to undergraduate students.
Category: Algebra

Replacements of recent Submissions

None