Mate and mutual mate functions in a seminearring

Manikandan G; Perumal R; Manikandan G; Perumal R

doi:10.3934/math.2020318

AIMS Mathematics

2020, Volume 5, Issue 5: 4974-4982. doi: 10.3934/math.2020318

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Research article

Mate and mutual mate functions in a seminearring

Manikandan G ,
Perumal R ^,

Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur-603203, Tamilnadu, India

Received: 10 February 2020 Accepted: 31 May 2020 Published: 09 June 2020
MSC : 16Y30, 16Y60

This work extends the concept of mate functions in nearrings to seminearrings and discusses the properties of mate functions. We obtain a complete characterisation of mate functions in a seminearring R. We show that every mate function φ of R gives rise to a mutual mate function for R. We derive a necessary and sufficient condition for a seminearring to possess a unique mutual mate function. We also obtain a necessary and sufficient condition for a seminearring to be a seminearfield vis-a-vis the behaviour of its mate functions.
- Mate function,
- Mutual mate function,
- Regular seminearring,
- Seminearfield
Citation: Manikandan G, Perumal R. Mate and mutual mate functions in a seminearring[J]. AIMS Mathematics, 2020, 5(5): 4974-4982. doi: 10.3934/math.2020318

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Abstract

This work extends the concept of mate functions in nearrings to seminearrings and discusses the properties of mate functions. We obtain a complete characterisation of mate functions in a seminearring R. We show that every mate function φ of R gives rise to a mutual mate function for R. We derive a necessary and sufficient condition for a seminearring to possess a unique mutual mate function. We also obtain a necessary and sufficient condition for a seminearring to be a seminearfield vis-a-vis the behaviour of its mate functions.

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