Mathematics and Statistics Vol. 11(5), pp. 816 - 819
DOI: 10.13189/ms.2023.110507
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MID-units in Right Duo-seminearrings

S. Senthil ^1,2, R. Perumal ^2,*
1 Department of Mathematics, Vels Institute of Science, Technology and Advanced Studies, India
² Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, India

ABSTRACT

In this paper, we focus on a subclass of duo-seminearrings called as right duo-seminearrings. We also focus on the algebraic properties and peculiarities of mid-units within this class. As a logical extension of the concept of mid-identities in semirings, the concept of mid-units in right pair seminearings is introduced. Mid-units are elements with both left and right invertibility, making them essential for understanding the structure and behaviour of right duo-seminearrings. In particular, we examine the interaction between idempotents and seminearring mid-units. We have also investigated regular right duo-seminearring which is a semilattice of subseminearrings with mid-units. In order to have a mid-unit in duo-seminearrings, we have established the necessary and sufficient conditions. The aim of this work is to carry out an extensive study on algebraic structure of right duo-seminearrings and the major objective is to further enhance the theory of right duo-seminearrings in order to find special structures of right duo-seminearrings. Throughout the research, rigorous proofs are provided to support the theoretical developments and ensure the validity of the findings. Concrete examples are also presented to illustrate the concepts and facilitate a better understanding of the algebraic structures associated with duo seminearings and mid-units. These examples serve as valuable tools for researchers and practitioners interested in the application of right duo-seminearrings and mid-units in their respective fields. Due to their applicability in domains such as computer science, cryptography, and coding theory, the topic of duo seminearrings, which generalise both semirings and duo-rings, have received substantial attention in algebraic research.

KEYWORDS
Right Duo, MID-units, Seminearring, Sub-seminearring, Idempotent

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] S. Senthil , R. Perumal , "MID-units in Right Duo-seminearrings," Mathematics and Statistics, Vol. 11, No. 5, pp. 816 - 819, 2023. DOI: 10.13189/ms.2023.110507.

(b). APA Format:
S. Senthil , R. Perumal (2023). MID-units in Right Duo-seminearrings. Mathematics and Statistics, 11(5), 816 - 819. DOI: 10.13189/ms.2023.110507.