Related papers: Further results on weighted core inverse in a ring

We introduce a model to design reflectors that take into account the inverse square law for radiation. We prove existence of solutions, both in the near and far field cases, when the input and output energies are prescribed.

The set of all subsets of any inverse semigroup forms an involution semiring under set-theoretical union and element-wise multiplication and inversion. We find structural conditions on a finite inverse semigroup guaranteeing that neither…

We discuss some mathematical aspects of the problem of inverting gravitational field data to extract the underlying mass distribution. While the forward problem of computing the gravity field from a given mass distribution is mathematically…

For $V$ a vector space over a field, or more generally, over a division ring, it is well-known that every $x\in\mathrm{End}(V)$ has an <i>inner inverse</i>, i.e., an element $y\in\mathrm{End}(V)$ satisfying $xyx=x.$ We show here that a…

We study those rings in which all invertible elements are weakly nil-clean calling them {\it UWNC rings}. This somewhat extends results due to Karimi-Mansoub et al. in Contemp. Math. (2018), where rings in which all invertible elements are…

Although there is no natural internal product for hermitian forms over an algebra with involution of the first kind, we describe how to multiply two $\varepsilon$-hermitian forms to obtain a quadratic form over the base field. This allows…

This paper presents a framework based on matrices of monoids for the study of coupled cell networks. We formally prove within the proposed framework, that the set of results about invariant synchrony patterns for unweighted networks also…

Ramified monoids are a class of monoids introduced by the authors. The main motivation for considering these monoids comes from knot theory, see [3, 4, 5]. Thus, in [2] we have studied the ramified monoids of the symmeytric group and of the…

The notion of derivation with invertible values as a derivation of ring with unity that only takes multiplicatively invertible or zero values appeared in a paper of Bergen, Herstein and Lanski, in which they determined the structure of…

In this paper, we discuss the inverse problem of determining a semisimple group algebra from the knowledge of rings of the type sum_{t=1}^s M_{n_t}(Ft), where j is an arbitrary integer and F_t is finite field for each t, and show that it is…

We prove that if an involution in a ring is the sum of an idempotent and a nilpotent then the idempotent in this decomposition must be 1. As a consequence, we completely characterize weakly nil-clean rings introduced recently in [Breaz,…

Invertibility is an important concept in category theory. In higher category theory, it becomes less obvious what the correct notion of invertibility is, as extra coherence conditions can become necessary for invertible structures to have…

In this article it is determined which integral reflection representations of the symmetric groups and the primitive complex reflection groups of degree $2$ have rings of invariants which are isomorphic to polynomial rings.

We consider an integral series f(X,t) which depends on the choice of a set X of labelled planar rooted trees. We prove that its inverse for composition is of the form f(Z,t) for another set Z of trees, deduced from X. The proof is…

We study generalized inverses on semigroups by means of Green's relations. We first define the notion of inverse along an element and study its properties. Then we show that the classical generalized inverses (group inverse, Drazin inverse…

The study of pinnacle sets has been a recent area of interest in combinatorics. Given a permutation, its pinnacle set is the set of all values larger than the values on either side of it. Largely inspired by conjectures posed by Davis,…

We introduce new concepts in order to develop a general formalism for twisted differential operators in several variables. We investigate the notion of twisted coordinates on Huber rings that allows us to build various rings of twisted…

In this paper, we present new presentations of group inverse for the sum of two group invertible elements in a Banach algebra. We then apply these results to block complex matrices. The group invertibility of certain block complex matrices…

We present some formulae for the Drazin inverse of difference and product of idempotents in a ring. A number of results of bounded linear operators in Banach spaces are extended to the ring case.

Irreducible cyclic codes are an interesting type of codes and have applications in space communications. They have been studied for decades and a lot of progress has been made. The objectives of this paper are to survey and extend earlier…