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On ideals in regular ternary semigroups

Tapan K. Dutta, Sukhendu Kar, Bimal K. Maity (2008)

Discussiones Mathematicae - General Algebra and Applications

In this paper we study some interesting properties of regular ternary semigroups, completely regular ternary semigroups, intra-regular ternary semigroups and characterize them by using various ideals of ternary semigroups.

On Lie semiheaps and ternary principal bundles

Andrew James Bruce (2024)

Archivum Mathematicum

We introduce the notion of a Lie semiheap as a smooth manifold equipped with a para-associative ternary product. For a particular class of Lie semiheaps we establish the existence of left-invariant vector fields. Furthermore, we show how such manifolds are related to Lie groups and establish the analogue of principal bundles in this ternary setting. In particular, we generalise the well-known ‘heapification’ functor to the ambience of Lie groups and principal bundles.

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