# 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

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### 1 Answer

**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.

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