CLEAR OBJECTS IN CATEGORIES OF COMMUTATIVE ALGEBRAS

The paper provides an answer to the following questions. What is an algebraic object in an arbitrary category of commutative algebras? And then, what is an algebraically closed object and an algebraic closure, if it exists? The answer is given by introducing the notion of clear objects obtained from the notion of neat objects by throwing off the separability property. It is shown that clear algebras share most of the properties of neat algebras, apart from separability.