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

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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

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Op. J. Math. Phys.
Volume 2, Article 120, 2020 [EQ]

A finite cancellative semigroup is a group

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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

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Op. J. Math. Phys.
Volume 2, Article 117, 2020 [EN]

A right zero semigroup is left-cancellative

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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

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Op. J. Math. Phys.
Volume 2, Article 116, 2020 [EM]

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

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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

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Op. J. Math. Phys.
Volume 2, Article 115, 2020 [EL]