Research Article Open Access

On the Construction and Properties of Lattice-Group Structure in Cartesian Product Spaces

Davronbek Malikov1 and Susmit Bagchi1
  • 1 Gyeongsang National University, Republic of Korea
Journal of Computer Science
Volume 16 No. 4, 2020, 402-421

DOI: https://doi.org/10.3844/jcssp.2020.402.421

Submitted On: 24 December 2019 Published On: 3 April 2020

How to Cite: Malikov, D. & Bagchi, S. (2020). On the Construction and Properties of Lattice-Group Structure in Cartesian Product Spaces. Journal of Computer Science, 16(4), 402-421. https://doi.org/10.3844/jcssp.2020.402.421

Abstract

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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Keywords

  • Lattice
  • Group
  • Lattice-Group
  • Partial Order
  • Monoid
  • Invertibility