Abstract

We describe the ∗-right annihilator  (∗-left anihilator) of a subset of a ring and we investigate the relationships between the right annihilator  and ∗-right annihilator. These connections permit the transfer of various properties from annihilators to ∗-annihilators . It is known that the quotient ring constructed from a ring and a maximal ideal is a field, whereas we prove that the quotient ring constructed from a ring and a *-maximal ideal is not a *-field. Equivalent definitions to ∗-regular ring are given.

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