Abstract
In [2], van der Walt has defined s-prime ideals in noncommutative rings and obtained analogous results of McCoy [1] for s-prime ideals. In the present paper, we shall give a generalized concept of prime ideals, called /-prime ideals, by using some family of ideals, and obtain analogous results in [2], If our family of ideals is, in particular, the set of principal ideals of the ring, the /-prime ideals coincide with the prime ideals and conversely. In addition, if we take multiplicatively closed systems as kernels, the /-prime ideals coincide with the s-prime ideals.
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