On hybrid  strong h-ideals and hybrid congruence of hemirings

V. Keerthika; G. Muhiuddin; Catherine G. John; B. Elavarasan

V. Keerthika Karunya Institute of Technology and Sciences, Coimbatore - 641114, Tamilnadu, India.
G. Muhiuddin University of Tabuk, P.O. Box-741, Tabuk-71491, Saudi Arabia.
Catherine G. John Karunya Institute of Technology and Sciences, Coimbatore - 641114, Tamilnadu, India.
B. Elavarasan Karunya Institute of Technology and Sciences, Coimbatore - 641114, Tamilnadu, India.

Abstract

In this article, we propose the idea of hybrid congruences and hybrid strong $\mathfrak{h}-$ideals of hemirings and we build an example that every hybrid strong $\mathfrak{h}-$ideal is an hybrid $\mathfrak{h}-$ideal, but not conversely. The hybrid hemiring homomorphisms and quotient rings through the hybrid strong $\mathfrak{h}-$ideals are also discussed. In addition, we look into the relationship between hybrid congruence and hybrid strong $\mathfrak{h}-$ideals of hemirings.