query: Why is a monoid with right identity and left inverse not necessarily a group?
positive_passages.docid: 19683
positive_passages.text: Is a semigroup $G$ with left identity and right inverses a group?
negative_passages.docid: 79478
negative_passages.text: Name for categorical product inside a monoid
negative_passages.docid: 29538
negative_passages.text: Does a non-abelian semigroup without identity exist?
negative_passages.docid: 93040
negative_passages.text: $f$ is surjective iff it has a right inverse: using the axiom of choice and errors in ProofWiki
negative_passages.docid: 107378
negative_passages.text: If a ring element is right-invertible, but not left-invertible, then it has infinitely many right-inverses.
negative_passages.docid: 120495
negative_passages.text: Does this correctly interpret the "$\cong$" between groups as "$=$" between sets?
negative_passages.docid: 120254
negative_passages.text: Nowhere commutative semigroups = rectangular bands?
negative_passages.docid: 62286
negative_passages.text: Suppose $G$ is a semigroup and it holds both left and right cancellation.
negative_passages.docid: 151009
negative_passages.text: semigroup in which Green's relations are different
negative_passages.docid: 44100
negative_passages.text: Prove that identity element is unique
negative_passages.docid: 58190
negative_passages.text: Definition of a monoid: clarification needed
negative_passages.docid: 128711
negative_passages.text: $(\Bbb Z\oplus \Bbb Z)[X] \not\cong \Bbb Z[X]\oplus \Bbb Z[X]\,$?
negative_passages.docid: 35408
negative_passages.text: What is the correct name for a "product function" on a monoid?
negative_passages.docid: 107900
negative_passages.text: A ring which has many distinct left inverses
negative_passages.docid: 28676
negative_passages.text: Is a finite group uniquely determined by the orders of its elements?
negative_passages.docid: 23517
negative_passages.text: Presentation $\langle x,y,z\mid xyx^{-1}y^{-2},yzy^{-1}z^{-2},zxz^{-1}x^{-2}\rangle$ of group equal to trivial group
negative_passages.docid: 17997
negative_passages.text: Right identity and Right inverse implies a group