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[11] viXra:2204.0171 [pdf] replaced on 2022-05-03 21:00:50
Authors: Luca Pettinari
Comments: 8 Pages.
A decomposition formula for an antisymmetric matrix Aω ∈ A3(R) is provided, where its axial
vector is expressed as ω = Mν, with M symmetric and ν ∈ R3. The proof is based mainly on
vector projection through Frobenius inner product. In the end, a vectorial identity involving cross
product is proved as a corollary of the decomposition formula.
Category: Algebra
[10] viXra:2204.0125 [pdf] submitted on 2022-04-21 10:32:30
Authors: Lucian M Ionescu
Comments: 4 Pages. With SAGE / CoCalc support for computations.
We investigate the zeros of the Betti portion of the Weil rational zeta function
for elliptic curves, towards a direct understanding of the Weil conjectures.
Examples are provided and various directions of investigations are considered.
Category: Algebra
[9] viXra:2204.0124 [pdf] submitted on 2022-04-21 11:09:09
Authors: Lucian M Ionescu
Comments: 21 Pages.
We review and comment on the Weil conjectures.
Category: Algebra
[8] viXra:2204.0123 [pdf] submitted on 2022-04-21 11:26:31
Authors: Lucian M Ionescu
Comments: 25 Pages.
The article aims to motivate the study of the relations between the Riemann zeros,
and the zeros of the Weil polynomial of a hyper-elliptic curve over finite fields,
beyond the well-known formal analogy.
The non-trivial distribution of the p-sectors of the Riemann spectrum recently studied by various authors,
represent evidence of a yet unknown algebraic structure exhibited by the Riemann spectrum,
supporting the above investigations.
This preparatory article consists essentially in a review of the topics involved,
and the ``maize'' of relationships to be clarified subsequently.
Examples are provided and further directions of investigation are suggested.
It is, if successful, a viable, possibly new approach to proving the Riemann Hypothesis,
with hindsight from the proof in finite characteristic and function fields.
Category: Algebra
[7] viXra:2204.0109 [pdf] submitted on 2022-04-18 05:55:54
Authors: Santosh Kumar Pandey
Comments: 3 Pages. Liense:NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
In this paper we consider a result on rings in which each element is a sum of two idempotents ( appeared in [1] ) and we improve the result by providing a counterexample.
Category: Algebra
[6] viXra:2204.0108 [pdf] submitted on 2022-04-18 06:03:37
Authors: Santosh Kumar Pandey
Comments: 3 Pages. Liense:NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
In this paper we provide an important and significant observation on a result related to
invo-regular rings [1].
Category: Algebra
[5] viXra:2204.0104 [pdf] submitted on 2022-04-18 15:44:02
Authors: Lucian M Ionescu
Comments: 8 Pages.
Galois theory in the category of cyclic groups studies the automorphism groups of the cyclic group extensions and the corresponding Galois connection.
The theory can be rephrased in dual terms of quotients, corresponding to extensions, when viewed as covering maps.
The computation of Galois groups and stating the associated Galois connection are based on already existing work regarding the automorphism groups of finite p-adic groups.
The initial goals for developing such a theory were:
pedagogical, to introduce the basic language of Category Theory, while exposing the student to core ideas of Galois Theory, but also targeting
applications to the Galois Theory of cyclotomic extensions.
Some aspects of Abelian Class Field Theory and Anabelian Geometry are also mentioned.
Category: Algebra
[4] viXra:2204.0073 [pdf] submitted on 2022-04-13 04:26:29
Authors: Eckhard Hitzer
Comments: 17 Pages. E. Hitzer, On Factorization of Multivectors in Cl(2,1), byTo be published in Mathematical Methods in the Applied Sciences, 2022.
In this paper we consider general multivector elements of Clifford algebras Cl(2,1), and look for possibilities to factorize multivectors into products of blades, idempotents and exponentials, where the exponents are frequently blades of grades zero (scalar) to n (pseudoscalar). We will succeed mostly, with a minor open case remaining.
Category: Algebra
[3] viXra:2204.0062 [pdf] submitted on 2022-04-12 00:44:32
Authors: Eckhard Hitzer, Carlile Lavor, Dietmar Hildenbrand
Comments: To be published in Mathematical Methods in the Applied Sciences, 37 pages, (2022).
We extensively survey applications of Clifford Geometric algebra in recent years
(mainly 2019–2022). This includes engineering, electric engineering, optical fibers,
geographic information systems, geometry, molecular geometry, protein structure,
neural networks, artificial intelligence, encryption, physics, signal-, image- and video
processing, and software.
Category: Algebra
[2] viXra:2204.0043 [pdf] submitted on 2022-04-09 06:51:47
Authors: Pierre-Yves Gaillard
Comments: 2 Pages.
If X is a set, M its monoid of self-maps and P its power set, then P can be viewed as a left M-set L or as a right M-set R. We compute the monoids End L and End R.
Category: Algebra
[1] viXra:2204.0013 [pdf] submitted on 2022-04-02 20:45:35
Authors: Santosh Kumar Pandey
Comments: 4 Pages. This paper offers substantial result in Algebra (Ring Theory).
In this note, some important observations have been reported on recent works related to strongly invo-clean rings [1-3].
Category: Algebra
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