The present paper continues my investigations [2]. For the rings satisfying the conditions (II)
and (21)(see § 2 below) one can build almost all the theory known for the/>-primary abelian …

LECTURES ON RINGS AND MODULES Page 1 BOOK REVIEWS 759 Karlin and various
collaborators. For a good many theorems alternative proofs (usually with a geometrical …

We assume all rings to be associative with non-zero units. The module Μ is called
distributive if the lattice L {M) of its submodule is distributive. The direct sum of distributive …

All rings are assumed to be associative and (except for nil-rings and for some stipulated
cases) with nonzero identity element. Given a module M over a ring A, we denote by/:(M) the …

Introduction. The problem considered is a special case of the general problem of the extent
to which a module (F, A) is determined by its endomorphism ring E (F, A). We restrict our …

3, From (2.3) we also see that conversely the regularity of Z implies that of A. It is of interest
to decide, whether these results may be given a more general setting; in particular, whether …

All rings considered in this paper are associative with an identity element and all modules
are unitary. Homomorphisms of right modules will be wirtten on the left hand side. We shall …

Let A be an associative ring which possesses a unit element t and. satisfies the minimum
condition for left ideals. Recently NAGAO-NAKAYA~ IA [9] have determined the structure of …

We introduce a symmetry property for unit-regular rings as follows: a∈ R is unit-regular if
and only if aR⊕(a− u) R= R (equivalently, Ra⊕ R (a− u)= R) for some unit u of R if and only …