@article {10.3844/jcssp.2020.402.421, article_type = {journal}, title = {On the Construction and Properties of Lattice-Group Structure in Cartesian Product Spaces}, author = {Malikov, Davronbek and Bagchi, Susmit}, volume = {16}, number = {4}, year = {2020}, month = {Apr}, pages = {402-421}, doi = {10.3844/jcssp.2020.402.421}, url = {https://thescipub.com/abstract/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.}, journal = {Journal of Computer Science}, publisher = {Science Publications} }