ziad1985 said:ps:if you come across on notes for Model theory it would be great too,thx.
Ring theory is a branch of abstract algebra that studies the properties of rings, which are mathematical structures consisting of a set of elements and two operations, addition and multiplication.
Ring theory has many applications in fields such as number theory, combinatorics, cryptography, and computer science. It is also used in physics, specifically in the study of symmetries and conservation laws.
A ring is a set of elements with two operations, addition and multiplication, whereas a field is a set of elements with the operations of addition, multiplication, division, and subtraction. In a field, every nonzero element has a multiplicative inverse, while in a ring, this is not always the case.
Some important properties of rings include associativity, distributivity, commutativity, and the existence of an identity element for both addition and multiplication. Rings can also have additional properties, such as being commutative or having a multiplicative identity element.
Ring theory is closely related to other branches of mathematics, such as group theory and field theory. In fact, rings can be seen as a generalization of groups and fields, and many concepts and theorems in ring theory have analogues in these other areas of mathematics.