Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-06-13T07:36:55.742Z Has data issue: false hasContentIssue false

# Appendix

Published online by Cambridge University Press:  22 August 2009

## Summary

This appendix gives a brief summary of facts needed from lattice theory, homological algebra and logic, with references to proofs or sometimes the proofs themselves. In each section some reference books are listed, with an abbreviation which is used in quoting them in the appendix.

Lattice theory

LT: G. Birkhoff, Lattice Theory, 3rd Edition. Amer. Math. Soc. Providence RI 1967.

BA: P. M. Cohn, Basic Algebra, Groups, Rings and Fields. Springer, London 2002.

FA: P. M. Cohn, Further Algebra and Applications. Springer, London 2003.

UA: P. M. Cohn, Universal Algebra, 2nd Edition. D. Reidel, Dordrecht 1981.

1. (i) We recall that a lattice is a partially ordered set in which any pair of elements a, b has a supremum (i.e. least upper bound, briefly: sup), also called join and written ab, and an infimum (i.e. greatest lower bound, briefly: inf), also called meet and written a ∨ b. It follows that in a lattice L every finite non-empty subset has a sup and an inf; if every subset has a sup and an inf, L is said to be complete. A partially ordered set that is a lattice (with respect to the partial ordering) is said to be lattice-ordered. It is possible to define lattices as algebras with two binary operations ∨,∧ satisfying certain identities, so that lattices form a variety of algebras (LT, p. 9, UA, p. 63 or BA, Section 3.1).

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2006

## Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

# Save book to Kindle

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

• Appendix
• Book: Free Ideal Rings and Localization in General Rings
• Online publication: 22 August 2009
• Chapter DOI: https://doi.org/10.1017/CBO9780511542794.013
Available formats
×

# Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

• Appendix
• Book: Free Ideal Rings and Localization in General Rings
• Online publication: 22 August 2009
• Chapter DOI: https://doi.org/10.1017/CBO9780511542794.013
Available formats
×

# Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

• Appendix
• Book: Free Ideal Rings and Localization in General Rings
• Online publication: 22 August 2009
• Chapter DOI: https://doi.org/10.1017/CBO9780511542794.013
Available formats
×