Probs. 12 & 13 , Sec. 2.3, in Herstein's TOPICS IN ALGEBRA, 2nd ed: Existence of only right-sided identity and right-sided inverses suffice
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To prove in a Group Left identity and left inverse implies right identity and right inverse
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If an element has a unique right inverse, is it invertible?
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Does a non-abelian semigroup without identity exist?
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Algebra struggles: 2 problems in 1
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prove that $f:X\rightarrow Y$ is surjective if and only if $f(f^{-1}(C))=C$
46875
The identity morphism in $\mathbf{Set}$ is the identity function
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a second course in abstract algebra
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Solved Problems in Algebraic Number Theory
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Things around $(\forall x)(\Psi \Rightarrow \Phi) \Leftrightarrow ((\exists z)\Psi) \Rightarrow \Phi)$
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Axiom of Choice and Right Inverse
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Finishing a proof: $f$ is injective if and only if it has a left inverse
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An automorphism that has no fixed points except for the identity and is its own inverse implies commutativity
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Prove that the multiplicative inverse of $a$ modulo $m$ exists if and only if $a$ and $m$ are coprime.
24657
Let $T,S$ be linear transformations, $T:\mathbb R^4 \rightarrow \mathbb R^4$, such that $T^3+3T^2=4I, S=T^4+3T^3-4I$. Comment on S.
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An identity which applies to all of the natural numbers
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Algebraic proof for the identity $\sum_{k=0}^m(-1)^{m-k}{{n \choose {k}}}= {{n-1}\choose m}$
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Identity type between A and B being non-empty implies non-emptiness of A and B?