Hello, I am currently taking course on an introduction to ring theory and I am having problems understanding what a isomorphism is. I can't follow the definition in Schuam's Outlines for isomorphism and the definition that was given in my lecture was brief and vague. If anyone can tell me: First what is an isomorphism between two systems? (An algerbraic system being defined as a set S together with any relations and operations defined on S). Secondly, how can I identify if two systems are isomorphic? Any help is appreciated. Thankyou.