Abstract
We introduce both for modules and rings classes of elements that are strongly connected to commutativity classes as defined in Abdi, M., Leroy, A. G. (2021). Graphs of commutatively closed sets. Linear Multilinear Algebra. 70(21):6965–6977 and Alghazzawi, D., Leroy, A. G. Commutatively closed sets in rings. Commun. Algebra. 47(4):1629–1641. We define a graph structure on the classes leading to a notion of distance for elements of a class. Examples are presented all along the paper, showing the interest of the notions.
Acknowledgments
We would like to thank the anonymous referee for her/his careful reading of the manuscript and useful comments. Part of this work was carried out while Mehrdad Nasernejad, in 2021, was invited CNRS Researcher at the Fédération de Recherche Mathématique des Hauts-de-France (FR2037 CNRS), working at the Laboratoire de Mathématiques de Lens of the Université d’Artois (France).