A ring R is called left morphic if, for each a E R, RI Ra 1(a) or equivalently thereexists b IE Rsuch thatRa = 1(b) and a) Rb,where denote the leftannihilators of a and b in R, respectively. Motivated by recent work on left morphicrings, we study the rings R satisfying the property that for each 0 IU a iE R there exists aunique b iE Rsuch that Ra =1(b)and a) Rb.These rings are completely determinedin this paper. We also completely determine the rings R with the property that for each0iI a IE R there exists a unique b E R such thatRa = 1(6).
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机译：如果对于每个E R，RI Ra 1（a）或同等地存在b IE R使得Ra = 1（b）和a）Rb分别代表R中的a和b的左an灭者，则将环R称为左晶。出于最近对左视变环的研究的启发，我们研究了满足以下性质的环R：对于每个0 IU a iE R，存在一个唯一的b iE R，使得Ra = 1（b）和a）Rb。这些环在本文中已完全确定。我们还完全确定了环R，其性质为：对于每个IE R，都存在一个唯一的b E R，使得Ra = 1（6）。
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