الفهرس 
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Abstract
The consistent way of investigating rings with involution, brie y -rings is to study them in the category of -rings with morphisms preserving also involution. In this thesis we continue the study of -rings and begin by introducing the class of -Baer -rings. This class is de ned by using - annihilators (instead of right annihilators) to get principal -biideals (instead of principal right ideals) and it naturally extends the class of Baer -rings. The use of -biideals makes this de nition consistent with involution than the use of right ideals in the notion of Baer -rings. We prove that each Baer -ring is semiprime. Moreover, we show that the property of -Baer extends to both the -corner and the center of the -ring. Furthermore, we discuss the relation between -Baer and quasi-Baer -rings. Also we give a generalization for the class of -IFP rings; that is the class of quasi-IFP rings.