S. N. Begum, Department of Mathematics, ShahJalal University of Science and Technology, Sylhet 3114, Bangladesh, e-mail: snaher@yahoo.com; A. S. A. Noor, Department of Mathematics and Physics, East West University, 43 Mohakhali, Dhaka 1212, Bangladesh, e-mail: noor@ewubd.edu
Abstract: A meet semilattice with a partial join operation satisfying certain axioms is a JP-semilattice. A PJP-semilattice is a pseudocomplemented JP-semilattice. In this paper we describe the smallest PJP-congruence containing a kernel ideal as a class. Also we describe the largest PJP-congruence containing a filter as a class. Then we give several characterizations of congruence kernels and cokernels for distributive PJP-semilattices.
Keywords: semilattice, distributivity, pseudocomplementation, congruence, kernel ideal, cokernel
Classification (MSC 2010): 06A12, 06B10, 06B99, 06D15
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