A ring monomorphism is an injective ring homomorphism. Equivalently, a ring homomorphism is a ring monomorphism iff its ring kernel is the zero ideal.
Ring Monomorphism
See also
Injection, Ring Endomorphism, Ring Homomorphism, Ring IsomorphismExplore with Wolfram|Alpha
References
Dummit, D. S. and Foote, R. M. "Ring Homomorphisms and Quotient Rings." §7.3 in Abstract Algebra, 3rd ed. Hoboken, NJ: Wiley, pp. 239-250, 2004.Cite this as:
Weisstein, Eric W. "Ring Monomorphism." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RingMonomorphism.html