Kyungpook Mathematical Journal 2005; 45(1): 21-31
Published online March 23, 2005
Copyright © Kyungpook Mathematical Journal.
On Semirings which are Distributive Lattices of Rings
S. K. Maity
Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata-700019, India
We introduce the notions of nilpotent element, quasi-regular element in a semiring which is a distributive lattice of rings. The concept of Jacobson radical is introduced for this kind of semirings.
Keywords: skew-ring, nilpotent semiring, quasi-regular element, regular ideal, semisimple semiring