We introduce the concepts of a ring of (von Neumann) regular range 1, a ring of semihereditary range 1, a ring of regular range 1. We find relationships between the introduced classes of rings and known ones for abelian and duo rings. We proved that Hermite duo ring of Gelfand range 1 is an elementary divisor ring.
Department of Algebra and Logic
Faculty of Mechanics and Mathematics
Ivan Franko National University of L'viv
1 Universytetska Str., 79000 Lviv, Ukraine
Tel: (+380 322) 394 172
E-mail: oromaniv at franko.lviv.ua