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Prime Ideals in Right Complement Bounded Rings
Hamed E. A BULKHEIR ..et al. KYUNGPOOK UNIVERSITY 1996 Kyungpook mathematical journal Vol.36 No.1
A ring R is right complement bounded (strongly right bounded) if every nonzero right complement (right ideal) contains a nonzero two-sided ideal. For these rings we discuss the set of nilpotent elements and show that the right singular ideal Z_(n) and its closure Z_(2) are completely prime. Furthermore the inessential prime ideals and the inessential maximal right ideals are described. A decomposition of a right continuous strongly right bounded ring with unity and no infinite sets of orthogonal central idempotents is given.