We consider the symmetric inverse monoid Zn of an n-element chain and its inverse submonoids VOI n , VOVI n , VOVl n and VO1H n of all order-preserving, order-preserving or order-reversing, orientation-preserving and orientation-preserving or orientation-reversing transformations, respectively, and give descriptions of their Abelian kernels relative to decidable pseudovarieties of Abelian groups.
Let H be a pseudovariety of abelian groups corresponding to a recursive supernatural number. In this note we explain how a concrete implementation of an algorithm to compute the kernel of a finite monoid relative to H can be achieved. The case of the pseudovariety Ab of all finite abelian groups was already treated by the second author and plays an important role here, where we will be interested in the proper subpseudovarieties of Ab. Our work relies on an algorithm obtained by Steinberg.
The current pandemic context has highlighted the importance of looking for technological alternatives that contribute for students to achieve greater autonomy in their learning. In particular, in the field of mathematics in higher education, it is urgent to find technological instruments that mediate learning, such as interactive content or online platforms.The MathE platform (https://mathe.pixel-online.org), still under development, aims to be a tool to facilitate the acquisition of mathematical skills in the field of higher education. Its main resources are the Self Need Assessment, Final Assessment, Material Didactic and Video Collection and are freely available for students and teachers. It was precisely the resource "Self Need Assessment", that served as the basis for a study with 84 students who attended the course unit of Linear Algebra and Analytical Geometry, as part of the 1st year of a Bachelor in engineering or technology in portuguese higher education. They solved some tasks of self-assessment on Vector Spaces and Linear Transformations, and finally answered a questionnaire in which they expressed their opinion of the platform.We intend to present the MathE platform and, based on the perceptions/opinions of students and teachers involved in the experiments carried out, analyse its potential for the promoting the teaching of linear algebra.
Abstract. The notion of kernel of a finite monoid relative to a pseudovariety of groups can be used to define relative solvability of monoids in a similar way to that the notion of derived subgroup can be used to define solvable group. In this paper we study the solvability of certain inverse monoids relative to pseudovarieties of abelian groups.
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