Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Logic

arXiv:1804.08136 (math)
[Submitted on 22 Apr 2018 (v1), last revised 15 May 2019 (this version, v3)]

Title:PBZ*-Lattices: Structure Theory and Subvarieties

Authors:Roberto Giuntini, Claudia Mureşan, Francesco Paoli
View PDF
Abstract:We investigate the structure theory of the variety of \emph{PBZ*-lattices} and some of its proper subvarieties. These lattices with additional structure originate in the foundations of quantum mechanics and can be viewed as a common generalisation of orthomodular lattices and Kleene algebras expanded by an extra unary operation. We lay down the basics of the theories of ideals and of central elements in PBZ*-lattices, we prove some structure theorems, and we explore some connections with the theories of subtractive and binary discriminator varieties.
Comments: 29 pages
Subjects: Logic (math.LO); Rings and Algebras (math.RA)
Cite as: arXiv:1804.08136 [math.LO]
  (or arXiv:1804.08136v3 [math.LO] for this version)
  https://doi.org/10.48550/arXiv.1804.08136

Submission history

From: Claudia Mureşan [view email]
[v1] Sun, 22 Apr 2018 16:54:59 UTC (35 KB)
[v2] Wed, 12 Dec 2018 15:45:37 UTC (28 KB)
[v3] Wed, 15 May 2019 01:46:13 UTC (28 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.LO
< prev   |   next >
new | recent | 2018-04
Change to browse by:
math
math.RA

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)