I need to learn some abstract algebra, and it's pretty hard doing this on my own. Please help me. According to the definition, Ring is an algebraic structure with two binary operations , commonly called addition (+) and multiplication ( . ). We write (R,+, .). Some examples of rings are: (Z, +, .), (2Z, +, .), (Q, +, .)etc... My problem is that where it is written (R,+,.), is + and . normal addition and multiplication respectively, or they're just some binary operations? If they were some binary operations, why they're saying that (Z, +, .) is a ring, without defining + and . ?? Sorry if my question were silly.