Nosratollah shajareh pourslavati

Document Type : Research Paper

Author

Department of Pure Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract

In this paper, a new structure for generalizing groups by limiting its binary operation to a subset of its domain is presented. For the set $G$, the function from $G \times G$ to G is called a binary operation. If we consider a subset of the Cartesian product $G \times G$, such as $P$, and limit the binary operation on G to P and denote it by the symbol $\ast$, we obtain a partial binary operation on $G$ . In fact, when $P= G \times G$ , then $\ast$ is a binary operation on $G$ . Therefore, when we have a partial binary operation, it may be $x \ast y$ or $y \ast x$ or both are not defined in G. In this generalization, some characteristics and a number of theorems and conclusions of group theory are examined and generalized.

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References

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Mathematics and Society
Volume 6, Issue 3 - Serial Number 3
September 2021
Pages 11-17

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History

  • Receive Date: 27 August 1400
  • Revise Date: 19 November 1400
  • Accept Date: 27 November 1400
  • Publish Date: 01 January 2024

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