Some special structures of S*and A* semirings

G Rajeswari; M Amala; T Vasanthi

doi:10.17485/IJST/v13i39.1702

Article

Some special structures of S*and A* semirings

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v13i39.1702

Year: 2020, Volume: 13, Issue: 39, Pages: 4109-4115

Original Article

Some special structures of Sand A semirings

G Rajeswari^1*, M Amala², T Vasanthi³

¹Research Scholar, Department of Applied Mathematics, Yogi Vemana University, Kadapa, 516003, Andhra Pradesh, India. Tel.: +91-63001 85834
²Assistant Professor, Department of Applied Mathematics, Sri Padmavati Mahila Visvavidyalayam, Tirupati, 517502, Andhra Pradesh, India
³Professor, Department of Applied Mathematics, Yogi Vemana University, Kadapa, 516003, Andhra Pradesh, India

*Corresponding Author
Tel: +91-63001 85834
Email: [email protected]

Received Date:19 September 2020, Accepted Date:18 October 2020, Published Date:07 November 2020

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: The main objective of this research article is to study the semiring structures, we have majorly focused on the constrains under which the structures of S*and A* semirings are additively and/or multiplicatively idempotent. We have also concentrated on the study of structures of totally ordered S* and A* semirings. Methods: We have imposed singularity, cancellation property, Integral Multiple Property (IMP) and some other constrains on both semirings. Findings: when we imposed totally ordered condition on these two semirings we observed that the additive structure takes place as a maximum addition. Applications: The proposed idempotents have wide applications to computer science, dynamical and logical systems, cryptography, graph theory and artificial intelligence.

Keywords: Almost idempotent; idempotent; integral multiple property; multiplicatively subidempotent; periodic; rectangular band; singular semigroup; zeroid

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Copyright

© 2020 Rajeswari et al.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).