On one-sided (B,C)-inverses of arbitrary matrices

[EN] In this article, one-sided $(b, c)$-inverses of arbitrary matrices as well as one-sided inverses along a (not necessarily square) matrix, will be studied. In addition, the $(b, c)$-inverse and the inverse along an element will be also researched in the context of rectangular matrices.Benítez López, J.; Boasso, E.; Jin, H. (2017). On one-sided (B,C)-inverses of arbitrary matrices. ELECTRONIC JOURNAL OF LINEAR ALGEBRA. 32:391-422. doi:10.13001/1081-3810.3487S3914223

One-sided generalized Drazin-Riesz and one-sided generalized Drazin-meromorphic invertible operators

The aim of this paper is to introduce and study left and right versions of the class of generalized Drazin-Riesz invertible operators, as well as left and right versions of the class of generalized Drazin-meromorphic invertible operators

Prime rings having one-sided ideal with polynomial identity coincide with special Johnson rings

AbstractThroughout R is a prime ring and is regarded as an algebra over its centroid. Let RΔ(ΔR) denote the right (left) singular ideal of R. R is called Johnson ring if it satisfies any of the two equivalent conditions: (a) RΔ = 0 = ΔR and R possesses uniform right and left ideals, (b) the right (left) quotient ring of R (in the sense of Utumi) is HomD(V, V) where V is a vector space over a division ring D. In addition if D is finite dimensional over its center then R is called a special Johnson ring. Denote by C the center of Utumi's right quotient ring of R. The results shown are: (1) R is a special Johnson ring iff there exists a nonzero one-sided ideal with polynomial identity (PI), (2) R has generalized polynomial identity (GPI) nontrivial over C iff each nonzero right (left) ideal of R contains a nonzero right (left) ideal with PI, (3) If R has GPI nontrivial over C then R cannot have nonzero nil one-sided ideals, (4) If R is integral domain the R has GPI nontrivial over C iff R has PI, (5) There does not exist a simple radical ring R satisfying a generalized polynomial identity nontrivial over the center of HomR(R, R), (6) R is a special Johnson ring with nonzero socle iff each nonnil right (left) contains an idempotent (≠0) and there exists a nonzero one-sided ideal with PI

One sided a_idempotent, one sided a_equivalent and SEP elements in a ring with involution

In order to study the properties of SEP elements, we propose the concepts of one sided a_idempotent and one sided a_equivalent. Under the condition that an element in a ring is both group invertible and MP_invertible, some equivalent conditions of such an element to be an SEP element are given based on these two concepts, as will as based on projections and the second and the third power of some products of some elements.Comment: 11 page

On Coreflexive Coalgebras and Comodules over Commutative Rings

In this note we study dual coalgebras of algebras over arbitrary (noetherian) commutative rings. We present and study a generalized notion of coreflexive comodules and use the results obtained for them to characterize the so called coreflexive coalgebras. Our approach in this note is an algebraically topological one.Comment: 39 page