Journal of Prime Research in Mathematics
Vol. 17 (2021), Issue 2, pp. 149 – 158
ISSN: 1817-3462E (Online) 1818-5495 (Print)
ISSN: 1817-3462E (Online) 1818-5495 (Print)
Isomorphism Theorems in Generalized d−algebras
Muhammad Anwar Chaudhry \(^a\), Muhammad Imran Qureshi \(^b\), Asfand Fahad\(^{c,*}\), Muhammad Sajjad Bashir\(^a\)
\(^a\)Department of Mathematics and Statistics, Institute of Southern Punjab, Multan, Pakistan.
\(^b\)Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari, Pakistan.
\(^c\)Center for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan.
\(^b\)Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari, Pakistan.
\(^c\)Center for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan.
Correspondence should be addressed to: imranqureshi18@gmail.com
Copyright © 2022 Muhammad Anwar Chaudhry, Muhammad Imran Qureshi, Asfand Fahad, Muhammad Sajjad Bashir. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Published: Received: 9 September 2021; Accepted:26 January 2022; Published Online: June 2022.
Abstract
We introduce the generalized d-algebras, generalized d-ideals (d∗-ideals, d#-ideals, d$-ideals) and other related notions. We also prove some properties about d-ideal, d#-ideal and results related to quotient generalized d-algebra. Through these constructions, we prove the first, second and the third isomorphism theorems for the generalized d-algebras. These developments contribute to the theory of the BCI/BCK/BCH and the generalized BCH-algebras.
Keywords:
Generalized d-algebras, Isomorphism theorems, BCH-algebras, d#-ideals.