Mathematics Department, University of Southwestern Louisiana
P.O.Box 41010, Lafayette, La 70504 USA
Department of Mathematics, University of Port Elizabeth
P.O.Box 1600, Port Elizabeth, 6000 South Africa
Abstract: We investigate the relationships between the ideal structure and the $*$-ideal structure of a ring with involution ($*$). Descriptions of $*$-minimal and $*$-maximal ideals are obtained in terms of minimal and maximal ideals, respectively. Furthermore conditions are provided allowing us to associate with each minimal or maximal ideal a $*$-minimal or $*$-maximal ideal, respectively. These connections are strong enough to permit the transfer of various properties from the $*$-ideal structure to the ideal structure or vice-versa.
Full text of the article: