Quasiregularity and Primitivity Relative to Right Ideals of a Ring

Strongly) Π- Regular Rings Relative to Right Ideal)

“…The notion of rings relative to right ideal, was first introduced by V. A. Andrunakievich and Yu. M. Ryabukhin in 1987 [2]. They studied the concepts of quasi-regularity and primitivity of rings relative to right ideal.…”

“…Later, V. A. Andrunakievich and A. V. Andrunakievich in 1991 [1], studied the concept of regularity of rings relative to right ideal as generalization of (Von Neumann) regular ring (also known as  P regular rings). A number of interesting papers have been published on this concept in recent years, e.g., [1], [2], [3], [5]. A ring R is called regular relative to right ideal [2].…”

“…A number of interesting papers have been published on this concept in recent years, e.g., [1], [2], [3], [5]. A ring R is called regular relative to right ideal [2]. In [2] it is proved that any ring R is regular relative to any maximal right ideal of R , [2, Corollary 2].…”

“…A ring R is called regular relative to right ideal [2]. In [2] it is proved that any ring R is regular relative to any maximal right ideal of R , [2, Corollary 2]. Also, it is proved that a ring R is regular relative to right ideal R P  if and only if for every R a  ,…”