Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Two Open Problems on CA-Groupoids and Cancellativities of T2CA-Groupoids
View through CrossRef
Cyclic associative groupoids (CA-groupoids) and Type-2 cyclic associative groupoids (T2CA-groupoids) are two types of non-associative groupoids which satisfy cyclic associative law and type-2 cyclic associative law, respectively. In this paper, we prove two theorems that weak cancellativity is cancellativity and right quasi-cancellativity is left quasi-cancellativity in a CA-groupoid, thus successfully solving two open problems. Moreover, the relationships among separativity, quasi-cancellativity and commutativity in a CA-groupoid are discussed. Finally, we study the various cancellativities of T2CA-groupoids such as power cancellativity, quasi-cancellativity and cancellativity. By determining the relationships between them, we can illuminate the structure of T2CA-groupoids.
Title: Two Open Problems on CA-Groupoids and Cancellativities of T2CA-Groupoids
Description:
Cyclic associative groupoids (CA-groupoids) and Type-2 cyclic associative groupoids (T2CA-groupoids) are two types of non-associative groupoids which satisfy cyclic associative law and type-2 cyclic associative law, respectively.
In this paper, we prove two theorems that weak cancellativity is cancellativity and right quasi-cancellativity is left quasi-cancellativity in a CA-groupoid, thus successfully solving two open problems.
Moreover, the relationships among separativity, quasi-cancellativity and commutativity in a CA-groupoid are discussed.
Finally, we study the various cancellativities of T2CA-groupoids such as power cancellativity, quasi-cancellativity and cancellativity.
By determining the relationships between them, we can illuminate the structure of T2CA-groupoids.
Related Results
A novel approach to AG-groupoids via soft intersection product operation
A novel approach to AG-groupoids via soft intersection product operation
This study investigates some general properties of soft sets on a symmetry-preserving structure AG-groupoid. Various weaknesses in the papers Karaaslan [22] and Sezgin [39] are re...
Topological fundamental groupoids: Brown's topology
Topological fundamental groupoids: Brown's topology
In this paper, we generalize the Brown$^{^,}$s topology on the fundamental groupoids. For a locally path connected space $X$ and a totally disconnected normal subgroupoid $M$ of $\...
Ample Groupoids, Topological Full groups, Algebraic K-theory Spectra and Infinite Loop Spaces
Ample Groupoids, Topological Full groups, Algebraic K-theory Spectra and Infinite Loop Spaces
Abstract
Inspired by work of Szymik and Wahl on the homology of Higman–Thompson groups, we establish a general connection between ample groupoids, topological full groups, algeb...
Symmetries in reversible programming: from symmetric rig groupoids to reversible programming languages
Symmetries in reversible programming: from symmetric rig groupoids to reversible programming languages
The Pi family of reversible programming languages for boolean circuits is presented as a syntax of combinators witnessing type isomorphisms of algebraic data types. In this paper, ...
Profesor Stanisław Batawia
Profesor Stanisław Batawia
The editor-in-chief of „Archiwum Kryminologii”, professor Stanisław Batawia, full member of the Polish Academy of Sciences, Professor of Warsaw University and of the Institute of ...
AF Embeddability of the C*-Algebra of a Deaconu-Renault Groupoid
AF Embeddability of the C*-Algebra of a Deaconu-Renault Groupoid
<p>We study Deaconu-Renault groupoids corresponding to surjective local homeomorphisms on locally compact, Hausdorff, second countable, totally disconnected spaces, and we c...
Minimal Inclusions of C*-algebras of Groupoids
Minimal Inclusions of C*-algebras of Groupoids
<p><strong>A non-degenerate inclusion of C*-algebras B ⊂ A is considered minimal if the only fully normalised ideals are trivial. An ideal is fully normalised if the se...
Internal Categorical Structures and Their Applications
Internal Categorical Structures and Their Applications
While surveying some internal categorical structures and their applications, it is shown that triangulations and internal groupoids can be unified as two different instances of the...