Oriented Steiner quasigroups

Izabella Stuhl

doi:10.1142/S0219498814500728

Oriented Steiner quasigroups

Izabella Stuhl

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We introduce the notion of an oriented Steiner quasigroup and develop elements of a relevant algebraic apparatus. The approach is based upon (modified) Schreier-type f-extensions for quasigroups (cf. earlier works [10, 11, 14]) achieved through oriented Steiner triple systems. This is done in a fashion similar to one in [13] where an analogous construction was established for loops. As a justification of this concept we briefly discuss an application of oriented Steiner triple systems in cryptography using oriented Steiner quasigroups.

Original language	English (US)
Article number	1450072
Journal	Journal of Algebra and its Applications
Volume	13
Issue number	8
DOIs	https://doi.org/10.1142/S0219498814500728
State	Published - Dec 2014

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Applied Mathematics

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10.1142/S0219498814500728

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title = "Oriented Steiner quasigroups",

abstract = "We introduce the notion of an oriented Steiner quasigroup and develop elements of a relevant algebraic apparatus. The approach is based upon (modified) Schreier-type f-extensions for quasigroups (cf. earlier works [10, 11, 14]) achieved through oriented Steiner triple systems. This is done in a fashion similar to one in [13] where an analogous construction was established for loops. As a justification of this concept we briefly discuss an application of oriented Steiner triple systems in cryptography using oriented Steiner quasigroups.",

author = "Izabella Stuhl",

note = "Funding Information: The author has been supported by FAPESP Grant — process No. 11/51845-5, and expresses her gratitude to IMS, University of S{\~a}o Paulo, Brazil, for the warm hospitality.",

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AB - We introduce the notion of an oriented Steiner quasigroup and develop elements of a relevant algebraic apparatus. The approach is based upon (modified) Schreier-type f-extensions for quasigroups (cf. earlier works [10, 11, 14]) achieved through oriented Steiner triple systems. This is done in a fashion similar to one in [13] where an analogous construction was established for loops. As a justification of this concept we briefly discuss an application of oriented Steiner triple systems in cryptography using oriented Steiner quasigroups.

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Oriented Steiner quasigroups

Abstract

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