Invo-regular unital rings
Journal Title: Annales Universitatis Mariae Curie-Skłodowska. Sectio A, Mathematica - Year 2018, Vol 72, Issue 1
Abstract
It was asked by Nicholson (Comm. Algebra, 1999) whether or not unit-regular rings are themselves strongly clean. Although they are clean as proved by Camillo–Khurana (Comm. Algebra, 2001), recently Nielsen and ˇSter showed in Trans. Amer. Math. Soc., 2018 that there exists a unit-regular ring which is not strongly clean. However, we define here a proper subclass of rings of the class of unit-regular rings, called invo-regular rings, and establish that they are strongly clean. Interestingly, without any concrete indications a priori, these rings are manifestly even commutative invo-clean as defined by the author in Commun. Korean Math. Soc., 2017.
Authors and Affiliations
Peter Danchev
Keywords
Related Articles
- EP ID EP530443
- DOI 10.17951/a.2018.72.1.45
- Views 106
- Downloads 0
On almost complex structures from classical linear connections
Let Mfm be the category of m-dimensional manifolds and local diffeomorphisms and let T be the tangent functor on Mfm. Let V be the category of real vector spaces and linear maps and let Vm be the category of m-dimension...
Note about sequences of extrema (A,2B)-edge coloured trees
In this paper we determine successive extremal trees with respect to the number of all (A,2B)-edge colourings.
Oscillation of third-order delay difference equations with negative damping term
The aim of this paper is to investigate the oscillatory and asymptotic behavior of solutions of a third-order delay difference equation. By using comparison theorems, we deduce oscillation of the difference equation from...
Eccentric distance sum index for some classes of connected graphs
In this paper we show some properties of the eccentric distance sum index which is defined as follows ξd(G)=∑v∈V(G)D(v)ε(v). This index is widely used by chemists and biologists in their researches. We present a lower bo...
Spectral analysis of singular Sturm-Liouville operators on time scales
In this paper, we consider properties of the spectrum of a Sturm-Liouville operator on time scales. We will prove that the regular symmetric Sturm-Liouville operator is semi-bounded from below. We will also give some con...