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Vol 17 No 4 (2023): BAREKENG: Journal of Mathematics and Its Applications
Articles

SOME FUNDAMENTAL PROPERTIES OF HEAPS

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  • Dwi Mifta Mahanani,
  • Dewi Ismiarti
Dwi Mifta Mahanani
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Brawijaya University, Indonesia
Dewi Ismiarti
Mathematics Study Program, Faculty of Science and Technology, Maulana Malik Ibrahim State Islamic University Malang, Indonesia
DOI: https://doi.org/10.30598/barekengvol17iss4pp1927-1932
Published December 18, 2023
Keywords
  • Groups,
  • Heaps,
  • Mal’cev Identity,
  • Ternary Operation
How to Cite
[1]
D. Mahanani and D. Ismiarti, “SOME FUNDAMENTAL PROPERTIES OF HEAPS”, BAREKENG: J. Math. & App., vol. 17, no. 4, pp. 1927-1932, Dec. 2023.

Copyright (c) 2023 Dwi Mifta Mahanani, Dewi Ismiarti

Creative Commons License

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

Abstract

Heap is defined to be a non-empty set  with ternary operation  satisfying associativity, that is  for every   and satisfying Mal’cev identity, that is  for all . There is a connection between heaps and groups. From a given heap, we can construct some groups and vice versa. The binary operation of groups can be built by choosing any fixed element  of heap  and is defined by =[x,e,y] for any . Otherwise, for given a binary operation of group , we can make a ternary operation defined by  for every   On heaps, there are some notions which are inspired by groups, such as sub-heaps, normal sub-heaps, quotient heaps, and heap morphisms. On this study, we will associate sub-heaps and corresponding subgroups and discuss some properties of heap morphisms.

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