## UNIQUELY MORPHIC RINGS

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.9, sa.2, ss.267-274, 2010 (SCI İndekslerine Giren Dergi)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 9 Konu: 2
• Basım Tarihi: 2010
• Doi Numarası: 10.1142/s0219498810003914
• Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
• Sayfa Sayıları: ss.267-274

#### Özet

A ring R is called left morphic if, for each a is an element of R, R/Ra congruent to 1(a) or equivalently there exists b is an element of R such that Ra = 1(b) and 1(a) = Rb, where 1(a) and 1(b) denote the left annihilators of a and b in R, respectively. Motivated by recent work on left morphic rings, we study the rings R satisfying the property that for each 0 not equal a is an element of R there exists a unique b is an element of R such that Ra = 1(b) and 1(a) = Rb. These rings are completely determined in this paper. We also completely determine the rings R with the property that for each 0 not equal a is an element of R there exists a unique b is an element of R such that Ra = 1(b).