Aburawash

What is it about?

In this paper, we continue the study of *-rings and the notion of *-reduced *-rings is introduced and their properties are studied. We introduce also the class of *-Baer *-rings, in terms of *-annihilators and principal *-biideals, which naturally extends the class of Baer *-rings. However,the use of *-biideals makes this concept more consistent with the involution than the use of right ideals in the notion of Baer *-rings. .

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Why is it important?

The consistent way of investigating rings with involution, briefly *-rings, is to study them in the category of *-rings where all morphisms considered (and so also embeddings) have to preserve involution and only subrings which are closed under involution are admitted.

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