Proof. Let M be the largest strongly regular ideal of R. We first show that every nilpotent
element of R= R/M is a homomorphic image of a nilpotent element of R. Let à= a+ M be an …

Throughout this paper the letter R denotes an associative ring with 1, Id (R) denotes the set
of all idempotent elements of R, C (R) denotes the center of R, and Nil (R) denotes the set of …

Throughout this paper rings are associative rings with identity, ring extensions share the
same identity, and modules are unitary. We shall consider the following three questions that …

Throughout this paper, all rings are associative rings with identity. The prime radical of a ring
R and the set of nilpotent elements in R are denoted by P (R) and N (R), respectively. In this …

A ring A is called a P1-ring if aAa= aA for all a 2 A. The author's main results are the
following theorems. Theorem 6: For an arbitrary ring A with no nonzero nilpotent ideals the …

By Schur's Lemma in ring theory, if R is a ring and M is an irreducible left R-module, then the
endomorphism ring End (M) is a division ring. But there exists a ring R with reducible R …

Throughout this paper rings are understood to be commutative with 1, and subrings are
understood to have the same identity as their over-rings. Familiarity with the Utumi-Lambek …

A note on π-regular rings* Page 1 PU.MA Ser. A, Vol 3 (1992), No. 1–2, pp. 39–42 A note on
π-regular rings* Miroslav Ciric† and Stojan Bogdanovic‡ Dedicated to Professor S. Lajos on …

The connection between the-regularity of an associative ring with identity and the simplicity
of all of its prime factors has long been investigated by many authors. We prove, in this note …

A ring A is said to be strongly regular if for every element a∈ A, there exists an element b∈
A such that a= a2b (this is equivalent to the condition that every principal right ideal of the …