In order to find a suitable expression of an arbitrary square matrix over finite commutative ring, we prove that every such is always representable as sum potent and nilpotent at most two when the Jacobson radical ring has zero-square. This somewhat extends results ours in Linear Multilinear Algebra (2022) established for matrices considered on fields. Our main theorem also improves recent due ...

It is well–known that every system with commensurable delays can be assigned a finite spectrum by feedback, provided that it is spectrally controllable. In general, the feedback involves distributed delays, and it is defined in terms of a Volterra equation. In the case of multivariable time–delay systems, one would be interested in assigning not only the location of the poles of the closed–loop...

The algorithms for linear algebra in the Magma and Axiom computer algebra systems work over an arbitrary ring. For example, the implementation of Gaussian elimination for reducing a matrix to (reduced) row Echelon form works over any field that the user constructs. In contrast, Maple’s facilities for linear algebra in its LinearAlgebra package only work for specific rings. If the input matrix c...

An element a in ring R has gs-Drazin inverse if there exists b ? comm2(a) such that = b2a, ab Rqnil. For any s C(R), we completely determine when generalized matrix A Ks(R) over local inverse.

The aim of this paper is to propose a new family codes. We define over the ring R=∑^4_{s=0}v^s_5A_4, with v^5_5=v_5. derive its properties, generator matrix and Gray images. This codes illustrated by three applications.

A code over Gaussian or Eisenstein integer residue ring is an additive group of vectors with entries in this which closed under the action constant multiplication by integers. In paper, we define dual codes for and rings, consider construction self-dual codes. Because, uniqueness prime element decomposition holds same way as one-variable polynomial rings finite fields rational ring, provide eff...

Assorted analytical methods have been proposed for evaluating the performance of a slotted ring network. This paper proposes MGM (Matrix Geometric Method) to analyze the station buffer of a slotted ring for DT (Discrete-Time) queueing. The slotted ring is analyzed for infinite station buffer as a late arrival DT system. Utilizing the characteristics of 2-D Markov chain, various performance meas...

Just as the function ring case we expect the existence of the coefficient field for the integer ring. Using the notion of one element field in place of such a coefficient field, we calculate absolute derivations of arithmetic rings. Notable examples are the matrix rings over the integer ring, where we obtain some absolute rigidity. Knitting up prime numbers via absolute derivations we speculate...

Let T,U and V be rings with identity and M be a unitary (T,U)-bimodule, N be a unitary (U, V )bimodule, D be a unitary (T, V )-bimodule . We characterize homomorphisms and isomorphisms of the generalized matrix ring Γ = ( T M D 0 U N 0 0 V )

In this paper we present a distance-hereditary decomposition of optimal chordal rings of 2k nodes into a set of rings of 2k nodes, where k is the diameter. All the rings belonging to this set have the same length and their diameter corresponds to the diameter of the chordal ring in which they are embedded. The members of this embedded set of rings are non-disjoint and preserve the minimal routi...