Dorroh extensions of algebras and coalgebras, II
Lan You, Hui-Xiang Chen
TL;DR
This paper investigates the structure of Dorroh extensions in bialgebras and Hopf algebras, providing conditions for their formation and describing their ideals and subcoalgebras with concrete examples.
Contribution
It offers necessary and sufficient conditions for Dorroh extensions to be bialgebras or Hopf algebras, advancing the understanding of their algebraic and coalgebraic structures.
Findings
Conditions for Dorroh extensions to be bialgebras or Hopf algebras
Descriptions of ideals and subcoalgebras in Dorroh extensions
Explicit examples illustrating the structure of these extensions
Abstract
In this paper, we study Dorroh extensions of bialgebras and Hopf algebras. Let be both a Dorroh pair of algebras and a Dorroh pair of coalgebras. We give necessary and sufficient conditions for to be a bialgebra and a Hopf algebra, respectively. We also describe all ideals of Dorroh extensions of algebras and subcoalgebras of Dorroh extensions of coalgebras and compute these ideals and subcoalgebras for some concrete examples.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra · Commutative Algebra and Its Applications