Dorroh extensions of algebras and coalgebras, II

Abstract

In this paper, we study Dorroh extensions of bialgebras and Hopf algebras. Let $(H,I)$ be both a Dorroh pair of algebras and a Dorroh pair of coalgebras. We give necessary and sufficient conditions for $H{⋉}_{d}I$ 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.

14 pages