# A semigroup with a left identity and left inverse is a group

[pedagogical]

We translate the proof of the theorem stated in the title, accomplished by Prover9, into a human readable form.

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

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 222, 2021 [IS]

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

[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]

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

[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]

# A finite cancellative semigroup is a group

[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]

# A right zero semigroup is left-cancellative

[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]