# SOME FUNDAMENTAL PROPERTIES OF HEAPS

• 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
Keywords: Groups, Heaps, Mal’cev Identity, Ternary Operation

### 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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Published
2023-12-18
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.
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Articles