If $A,B$ are unital algebras, then for any homomorphism $\psi:A\rightarrow B$ we have $\psi(1_A)=1_B$. What can we say about structure of algebras $A,B$ if the preimage of $\{1_B\}$ is equal $\{1_A\}$ for any $\psi\in \mathrm{Hom}(A,B)$?
2026-03-26 10:41:08.1774521668
Preimage of unit in algebra
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