Another way to think about it is that a homomorphism is a map that commutes with multiplication, addition, scaling - or whatever operations characterize your algebraic object.

What does it mean when two things are homomorphic (its clear that when two things are isomorphic, they are essentially the same object with different labels)? $\endgroup$ – Madhav …

Isomorphisms capture "equality" between objects in the sense of the structure you are considering. For example, $2 \mathbb{Z} \ \cong \mathbb{Z}$ as groups, meaning we could re …

2015年11月2日 · $\begingroup$ Maybe you also want to mention that the term homomorphic is completely useless as any two groups will be homomorphic. $\endgroup$ – Tobias Kildetoft …

2023年7月21日 · $\begingroup$ "How are homomorphic images and homomorphisms different?" For starters a homomorphism is a function, while homomorphic image a subset. Have you …

The only ideals of a field are $(0)$ and $(1)=$ the field; therefore if homomorphic images of ideals were ideals, then $\phi(F) = (0)$ or $(1)$. Since $\phi(1) \neq 0$, we would have $\phi(F) = K$ …

2016年4月2日 · Isomorphic and Homomorphic. Ask Question Asked 9 years ago. Modified 9 years ago. Viewed 1k times ...

2018年7月19日 · In homomorphic image of Jacobson ring Nilradical is equal to the Jacobson radical. 0. The only non-trivial ...

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2016年8月26日 · Its homomorphic images therefore have order dividing 8, and the ones of order 1 and 8 are trivial (the ...