Idempotents in Matrix Rings

Rings with Many Idempotents

We introduce a new stable range condition and investigate the structures of rings with many idempotents. These are also generalizations of corresponding results of J. Stock and H. P. Yu.

IDEMPOTENTS IN GROUP RINGS By

It is then easily verified that RG satisfies the ring axioms; in fact, RG is a linear algebra over R. (We write all groups multiplicatively, and denote group identities by 1; we also use 1 for the unit element of R if there is one.) If R, in addition to being a ring, is a Banach algebra (i.e., an algebra over the complex field K, with a submultiplicative norm which makes R a Banach space), then...

Smarandache Idempotents in Loop Rings

In this paper we establish the existance of S-idempotents in case of loop rings ZtLn(m) for a special class of loops Ln(m); over the ring of modulo integers Zt for a specific value of t.These loops satisfy the conditions g 2 i = 1 for every gi ∈ Ln(m). We prove ZtLn(m) has an S-idempotent when t is a perfect number or when t is of the form 2p or 3p (where p is an odd prime) or in general when t...

Elements of Rings with Equal Spectral Idempotents

In this paper we define and study a generalized Drazin inverse x for ring elements x, and give a characterization of elements a, b for which aa = bb. We apply our results to the study of EP elements in a ring with involution. 2000 Mathematics subject classification: primary 16A32, 16A28, 15A09; secondary 46H05, 46L05.

Differential Polynomial Rings of Triangular Matrix Rings