[knowledge base]
RING, commutative ring, almost a ring, semiring, zero ring, zero property, zero divisors, domain, integral domain, and their underlying definitions are presented in this white paper (knowledge base).
https://doi.org/10.31219/osf.io/bzugr
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 216, 2021 [IM]
[knowledge base]
CYCLIC GROUP and its underlying definitions are presented in this white paper (knowledge base).
https://doi.org/10.31219/osf.io/nvkab
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 215, 2021 [IL]
[microreview]
We prove that a subgroup has the same number of left and right cosets.
https://doi.org/10.31219/osf.io/t4snh
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 137, 2020 [FH]
[white paper]
We propose a model to assign prime numbers to axioms and theorems, then by comparing equivalent numbers, it results in new equivalent theorems.
https://doi.org/10.31219/osf.io/wbf85
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 132, 2020 [FC]
[microreview]
We prove the proposition addressed in the title of this paper.
https://doi.org/10.31219/osf.io/98khs
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 120, 2020 [EQ]
[microreview]
We prove the proposition addressed in the title of this paper.
https://doi.org/10.31219/osf.io/7vm92
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 118, 2020 [EO]
[microreview]
We prove the proposition addressed in the title of this paper.
https://doi.org/10.31219/osf.io/34vbp
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 117, 2020 [EN]
[microreview]
We prove the proposition addressed in the title of this paper.
https://doi.org/10.31219/osf.io/g6snd
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 116, 2020 [EM]
[microreview]
We prove the proposition addressed in the title of this paper.
https://doi.org/10.31219/osf.io/zpwb5
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 115, 2020 [EL]
[question]
We present a sketch on a problem related to the isomorphism between the simple group of order 168 and the projective general linear group.
https://doi.org/10.31219/osf.io/ydex4
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 114, 2020 [EK]
[microreview]
We show that the permutation of six Sylow 5-subgroups by conjugation is a faithful action, so that G is isomorphic to a subgroup of S6.
https://doi.org/10.31219/osf.io/g43yj
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 113, 2020 [EJ]
[microreview]
We show within the maximum number of steps that if only one point is moved by two permutations, the commutator is a 3-cycle.
https://doi.org/10.31219/osf.io/kxnt8
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 106, 2020 [EC]
[original idea]
We apply in the complex numbers the same line of thought that led to the very creation of the complex themselves. In addition, we consider multiple imaginary numbers and generalize both ideas altogether.
https://doi.org/10.31219/osf.io/485kj
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 105, 2020 [EB]
[knowledge base]
We present a list of mathematical results for future implementation in a digital Open Mathematics Knowledge Base.
https://doi.org/10.31219/osf.io/evq8a
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 103, 2020 [DZ]
[microreview]
I present a collection of mathematical results regarding group theory organized by tags.
https://doi.org/10.31219/osf.io/9xk68
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 101, 2020 [DX]
[microreview]
Some definitions and results for counting with groups are presented within the fewest words and symbols as possible.
https://doi.org/10.31219/osf.io/9hdwj
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 100, 2020 [DW]
[microreview]
The purpose of this paper is organizational for it presents a list of notations and mathematical definitions used in some results of abstract algebra.
https://doi.org/10.31219/osf.io/u8yx2
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 98, 2020 [DU]
[microreview]
Some definitions and results of group actions are presented within the fewest words and symbols as possible.
https://doi.org/10.31219/osf.io/9dt34
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 97, 2020 [DT]
[microreview]
Some definitions and results of homomorphisms are presented within the fewest words and symbols as possible.
https://doi.org/10.31219/osf.io/7pgcs
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 95, 2020 [DR]
[microreview]
Some definitions and results of groups are presented within the fewest words and symbols as possible.
https://doi.org/10.31219/osf.io/bfyhm
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 93, 2020 [DP]
[original idea]
We address a discussion whether zero divides zero.
https://doi.org/10.31219/osf.io/5txzg
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 69, 2020 [CQ]
