Constructions of free dibands and tribands

Huang, Juwei; Bai, Yuxiu; Chen, Yuqun; Zhang, Zerui

doi:10.1007/s00233-022-10270-w

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2023

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“…For n = 2 (n = 3), the variety of n-tuple semigroups contains commutative dimonoids (commutative trioids). We remind that dimonoids and trioids were introduced in [14] and [15], respectively, and studied, e.g., in [11,23,24,26,31,32,34,43]. The algebras, which retained quite a few properties of 2-tuple semigroups, turned out to be bisemigroups [22] and restrictive bisemigroups [21].…”

Section: Introductionmentioning

confidence: 99%

Structure of relatively free n-tuple semigroups

Zhuchok

2023

ADM

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An n-tuple semigroup is an algebra defined on a set with n binary associative operations. This notion was considered by Koreshkov in the context of the theory of n-tuple algebras of associative type. The n>1 pairwise interassociative semigroups give rise to an n-tuple semigroup. This paper is a survey of recent developments in the study of free objects in the variety of n-tuple semigroups. We present the constructions of the free n-tuple semigroup, the free commutative n-tuple semigroup, the free rectangular n-tuple semigroup, the free left (right) k-nilpotent n-tuple semigroup, the free k-nilpotent n-tuple semigroup, and the free weakly k-nilpotent n-tuple semigroup. Some of these results can be applied to constructing relatively free cubical trialgebras and doppelalgebras.

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Section: Introductionmentioning

confidence: 99%

Structure of relatively free n-tuple semigroups

Zhuchok

2023

ADM

View full text Add to dashboard Cite

show abstract

Constructions of free dibands and tribands

Cited by 1 publication

References 13 publications

Structure of relatively free n-tuple semigroups

Structure of relatively free n-tuple semigroups

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