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Residue Classes Euclidean Ring Over Integral Domain of Gaussian Integers

Sujatha L.*, Srinivasa Rao T.**

*-** Department of Mathematics, UCST, AKNU, Andhra Pradesh, India.

Periodicity:July - December'2025

Abstract

Z√i = {m + in: m, n ∈ Z} is an integral domain under the addition defined by (m₁+in₁) ⊕ (m₂+in₂) = (m₁+_nm₂) + i(n₁+_nn₂) and multiplication defined by (m₁+in₁) ʘ (m₂+in₂) = (m₁m₂+_n(-n₁n₂)) + i(m₁n₂+_nn₁m₂). Taking n^th - degree polynomials taking coefficients from the integral domain of Gaussian integers and using the residue classes modulo n operation on this integral domain, the degree of the polynomial is used to define the ordering relation and create a partially ordered set and further, defining the same addition and multiplication operations to join and meet respectively, this integral domain can be verified as the not distributive lattice.

Keywords

Residue Classes Modulo n, Addition Modulo n, Multiplication Modulo n, Commutative Ring with Unity, Divisors of Zero.

How to Cite this Article?

Sujatha, L., and Rao, T. S. (2025). Residue Classes Euclidean Ring Over Integral Domain of Gaussian Integers. i-manager’s Journal on Mathematics, 14(2), 21-24.

References

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Residue Classes Euclidean Ring Over Integral Domain of Gaussian Integers

Abstract

Keywords

How to Cite this Article?

References

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