Congruences in seminearrings and their correspondence with strong ideals
نویسندگان
1 Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, India.
2 Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, India.
3 Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, India.
doi
10.22034/as.2024.3353چکیده
In this paper, we define the notion of strong ideal of a seminearring $S.$ If $S$ is a nearring or a ring then the concept of a strong ideal of $S$ coincides with the usual ideal of $S.$ We show that there is one-one correspondence between strong ideals of $S$ and strong congruences on $S$. Using the concept of strong ideals, we prove classical isomorphism theorems on $S$. We study insertion of factors property and obtain basic results on equisemiprime ideals.
