Free skew Boolean algebras-Reference-Cited by-同舟云学术

Free skew Boolean algebras

Published:2016-11 Issue:07 Volume:26 Page:1323-1348
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

Kudryavtseva Ganna¹,Leech Jonathan²

Affiliation:

1. Department of Civil and Geodetic Engineering, University of Ljubljana, Jamova Cesta 2, SI-1000 Ljubljana, Slovenia

2. Department of Mathematics, Westmont College, 955 La Paz Road, Santa Barbara, CA 93108, USA

Abstract

We study the structure and properties of free skew Boolean algebras (SBAs). For finite generating sets, these free algebras are finite and we give their representation as a product of primitive algebras and provide formulas for calculating their cardinality. We also characterize atomic elements and central elements, and calculate the number of such elements. These results are used to study minimal generating sets of finite SBAs. We also prove that the center of the free infinitely generated algebra is trivial and show that all free algebras have intersections.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196716500569

Reference23 articles.

1. A non-commutative Priestley duality

2. The axiomatization of override and update

3. Skew Boolean algebras and discriminator varieties

4. A Course in Universal Algebra

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Free Skew Boolean Intersection Algebras and Set Partitions;Order;2016-10-31

2. VARIETIES OF SKEW BOOLEAN ALGEBRAS WITH INTERSECTIONS;Journal of the Australian Mathematical Society;2016-09-09