maximal right ideals which make a new class of reversible rings

Reversible rings are presently the subject of very researches. in this article, we try to get some of the previous results about reversible rings under better conditions. for this purpose, we will introduce a class of reversible rings called right gr-ring. a ring r is said to be a right gr- ring, if every right ideal of r is a reversible right ideal. we will show that a vonneumann ring r is a right gr-ring, iff every maximal right ideal of r is a reversible right ideal. using this result, we obtain conditions in which subrings of a right gr-ring are right gr-rings.