A new branch of bialgebraic structures: UP-bialgebras. Issue 1 (11th December 2019)

• Record Type: Journal Article
• Authors: Mosrijai, Phakawat; Iampan, Aiyared
• Is Part Of: Journal of Taibah University for science. Volume 13:Issue 1(2019)
• Page Start: 450
• Page End: 459
• Publication Date: 2019-12-11
• Subjects: UP-algebra -- UP-bialgebra -- UP-bihomomorphism; 03G25; Science -- Periodicals; Science; Periodicals; 505
• DOI: 10.1080/16583655.2019.1592932
• Languages: English
• ISSNs: 1658-3655

Abstract

Abstract : The notion of bialgebraic structures was discussed by Vasantha Kandasamy [Bialgebraic structures and Smarandache bialgebraic structures. India: American Research Press; 2003]. The main target of this paper is to introduce the notions of a KU-bialgebra, a KP-bialgebra, a PK-bialgebra, and a UP-bialgebra and the notions of a UP-bisubalgebra, a UP-bifilter, a UP-biideal, and a strongly UP-biideal of UP-bialgebras, and prove the generalization of the notions and some results related to a UP-subalgebra, a UP-filter, a UP-ideal, and a strongly UP-ideal of UP-algebras. Furthermore, we introduce the notion of a UP-bihomomorphism and study the image and inverse image of a UP-bisubalgebra, a UP-bifilter, a UP-biideal, and a strongly UP-biideal of UP-bialgebras under a UP-bihomomorphism. Finally, we have the generalization diagram of KU/KP/PK/UP-bialgebras (see Figure 1) and the diagram of special subsets of UP-bialgebras (see Figure 2).