A ring with unity element in which every non-zero element has a multiplicative inverse is called1)Field 2)Skew field 3)Integral domain 4)None of these
Skew field (also called division ring) is non-trivial ring (meaning it doues not consist of only one element) in which every non-zero element has multiplicative inverse i.e. `forall x EE y (xy=yx=1)`. This also implies existance of identity element.
Thus your answer is 2) Skew field.
Also integral domain is comutative ring with identity in which product of non-zero elements is never zero. Integral domains are generalization of integers.
Field is commutative skew field. It can be shown that every finite skew field is commutative and thus field. There are other axiomatizations of field.
Ring is algebraic structure `(R,+,cdot)` where `R` is a set and `+` and `cdot` are binary operations called addition and multiplication. `(R,+)` is abelian group and multiplication is associative and distributive over addition.