The existing huge volume of algebraic structures in the subject “ALGEBRA” has few serious hidden gaps and needs fixing in order to validate many of the elementary and important frequently practiced algebraic computations

Biswas, Ranjit

Indonesian Journal of Mathematics and Applications
Vol. 4 No. 1 (2026): Indonesian Journal of Mathematics and Applications

In this paper it is justified in full length that there is a genuine need for the giant subject ‘ALGEBRA’ to have a new but unique Algebraic Structure. Consequently, a new algebraic structure “Region” is introduced, and its properties are studied. This paper introduces a new algebraic structure called Region, providing a unified framework for interactions between internal multiplication and scalar multiplication commonly used in algebra. The novelty lies in combining field structure, vector space structure, and compatibility in a single framework. Without the algebraic structure “Region” the subject ‘ALGEBRA’ can not validate many elementary algebraic computations being frequently practiced by the mathematicians, researchers and students in their daily works in the last centuries; unbelievable and surprising, but it is true.