On the Construction and Properties of Lattice-Group Structure in Cartesian Product Spaces
- 1 Gyeongsang National University, Republic of Korea
Copyright: © 2020 Davronbek Malikov and Susmit Bagchi. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
The lattice theory and group algebra have several applications in computing sciences as well as physical sciences. The concept of lattice-group structure is an interesting hybrid algebraic structure having potential applications. In this paper, the algebraic construction of lattice-group structure is formulated and associated algebraic properties are established. The proposed construction considers Cartesian product spaces. The concept of two-dimensional monoid is formulated in Cartesian product spaces of real numbers and a related lattice-group structure is established in the space having reduced dimension. The different categories of functions are employed for dimension reduction while establishing the lattice-group structure. The proposed lattice-monoid and lattice-group structures are finite in nature. The algebraic properties of lattice-group as well as associated structures are formulated. A set of numerical examples are presented in the paper to illustrate structural properties. Finally, the comparative analysis of the proposed structure with other contemporary work is included in the paper.
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