Indian Journal of Science and Technology
DOI: 10.17485/IJST/v17i12.3184
Year: 2024, Volume: 17, Issue: 12, Pages: 1143-1147
Original Article
Tilak Raj Sharma1*, Rajesh Kumar2
1Department of Mathematics, Himachal Pradesh University, Regional Centre, Dharamshala, 176218, Himachal Pradesh, India
2Department of Mathematics, Government Degree College, Dharamshala, 176215, Himachal Pradesh, India
*Corresponding Author
Email: [email protected]
Received Date:19 December 2023, Accepted Date:23 February 2024, Published Date:14 May 2024
Objectives: The main objective of this paper is to derive some of the results of lattice ordered semirings, distributive lattice, lattice ideals and morphisms. Methods: To establish the results, we use some conditions like commutativity, simple, multiplicative idempotent, additively idempotent, and finally, use the concept of lattice ideal in semirings. Findings: First we give some examples of lattice ordered semirings and then study some results regarding lattices, distributive lattices, commutative lattice ordered semirings and finally lattice ideals and morphisms. The unique feature of this study is that the concept of gamma is new for the study of lattices. Novelty: We consider a condition (c.f. Theorem 4.1.5) for an additively idempotent semiring due to which it becomes a distributive lattice ordered semiring. Again, in general, the sum of ideals of a semiring need not be ideal. Indeed, and are ideals of is a set of non-negative integers. Clearly, (say) is not a ideal, because , but . However, this condition does not hold in the case of a lattice ordered semiring. AMS Mathematics subject classification (2020): 16Y60.
Keywords: Lattices, additive idempotent, multiplicative Γ-idempotent, k-ideal, lattice ideal, Γ-morphism
© 2024 Sharma & Kumar. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)
Subscribe now for latest articles and news.