A linear algebra

[knowledge base]

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LINEAR ALGEBRA and its underlying definitions are presented in this white paper (knowledge base).

https://doi.org/10.31219/osf.io/8emp4

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 225, 2021 [IV]

Linear Transformations

[knowledge base]

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LINEAR TRANSFORMATION and its underlying definitions are presented in this white paper [knowledge base (http://omkb.org)].

doi.org/10.31219/osf.io/cjdwg

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 224, 2021 [IU]

Modules over Rings

[knowledge base]

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MODULES over RINGS and its underlying definitions are presented in this white paper (knowledge base).

https://doi.org/10.31219/osf.io/xjsc7

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 220, 2021 [IQ]

Vector space over a field

[knowledge base]

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VECTOR SPACE OVER A FIELD and its underlying definitions are presented in this white paper (knowledge base).

https://doi.org/10.31219/osf.io/g6ux5

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 219, 2021 [IP]

Field, commutative ring, integral domain

[knowledge base]

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FIELD, three propositions, and their underlying definitions are presented in this white paper (knowledge base).

https://doi.org/10.31219/osf.io/wmjst

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 217, 2021 [IN]

RINGS: Almost a ring, semiring, zero, integral domain

[knowledge base]

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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]

Cyclic Group

[knowledge base]

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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]

A subgroup has equally many left and right cosets

[microreview]

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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]

On the arithmetic of automated theorem proving

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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]

A semigroup is a rectangular band if and only if it is nowhere commutative

[microreview]

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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]

An element of a finite monoid is right invertible if and only if it is left invertible

[microreview]

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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]

A finite cancellative semigroup is a group

[microreview]

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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]

A right zero semigroup is left-cancellative

[microreview]

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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]

A semigroup with a right zero equal to a right identity is trivial

[microreview]

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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]

A simple group of order 168 is isomorphic to PGL(2,7)

[question]

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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]

A simple group of order 60 is isomorphic to a subgroup of S6

[microreview]

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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]

3-cycle commutator

[microreview]

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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]

Complex complex numbers

[original idea]

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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]

Open Mathematics Knowledge Base

[knowledge base]

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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]

Mathematical tags of group theory

[microreview]

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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]

Counting with groups: a concise approach

[microreview]

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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]