MID-units in Right Duo-seminearrings

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.