Skip to main content Accessibility help
×
Home
Hostname: page-component-5c569c448b-q9r9l Total loading time: 0.139 Render date: 2022-07-01T13:23:44.170Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

Shellability of semigroup rings

Published online by Cambridge University Press:  22 January 2016

Annetta Aramova
Affiliation:
FB6 Mathematik und Informatik, Universität – GHS – Essen, Postfach 103764, 45117 Essen, Germany, A.Aramova@uni-essen.de
Jürgen Herzog
Affiliation:
FB6 Mathematik und Informatik, Universität – GHS – Essen, Postfach 103764, 45117 Essen, Germany, juergen.herzog@uni-essen.de
Takayuki Hibi
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, 560-0043, Japan, hibi@math.sci.osaka-u.ac.jp
Rights & Permissions[Opens in a new window]

Abstract

HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The concepts of Λ-shellability of locally finite posets as well as of extendable sequentially Koszul algebras will be introduced. It will be proved that the divisor poset of a homogeneous semigroup ring is Λ-shellable if and only if the semigroup ring is extendable sequentially Koszul. Examples of extendable sequentially Koszul semigroup rings contain all monomial ASL’s (algebras with straightening laws) and all second squarefree Veronese subrings.

Keywords

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2002

References

[1] Björner, A., Shellable and Cohen-Macaulay partially ordered sets, Trans. Amer. Math. Soc., 260 (1980), 159183.CrossRefGoogle Scholar
[2] Björner, A. and Wachs, M., On lexicographically shellable posets, Trans. Amer. Math. Soc., 277 (1983), 323341.CrossRefGoogle Scholar
[3] Bruns, W. and Herzog, J., Cohen-Macaulay Rings, Cambridge University Press, Cambridge, New York, Sydney, 1993.Google Scholar
[4] Eisenbud, D., Introduction to algebras with straightening laws, Ring Theory and Algebra III (B. R. McDonald, ed.), Dekker, New York (1980), pp. 243268.Google Scholar
[5] Herzog, J., Hibi, T. and Restuccia, G., Strongly Koszul algebras, Math. Scand., 86 (2000), 161178.CrossRefGoogle Scholar
[6] Herzog, J., Reiner, V. and Welker, V., The Koszul property in affine semigroup rings, Pacific J. Math., 186 (1998), 3965.CrossRefGoogle Scholar
[7] Hibi, T., Algebraic Combinatorics on Convex Polytopes, Carslaw Publications, Glebe, N.S.W., Australia, 1992.Google Scholar
[8] Ohsugi, H., Herzog, J. and Hibi, T., Combinatorial pure subrings, Osaka J. Math., 37 (2000), 745757.Google Scholar
[9] Ohsugi, H. and Hibi, T., Toric ideals generated by quadratic binomials, Algebra J., 218 (1999), 509527.CrossRefGoogle Scholar
[10] Ohsugi, H. and Hibi, T., Compressed polytopes, initial ideals and complete multipartite graphs, Illinois J. Math., 44 (2000), 391406.Google Scholar
[11] Peeva, I., Reiner, V. and Sturmfels, B., How to shell a monoid, Math. Ann., 310 (1998), 379393.CrossRefGoogle Scholar
[12] Stanley, R., Enumerative Combinatorics, Volume I, Wadsworth & Brooks/Cole, Monterey, Calif., 1986.CrossRefGoogle Scholar
[13] Sturmfels, B., Gröbner Bases and Convex Polytopes, Amer. Math. Soc., Providence, RI, 1995.Google Scholar
You have Access
2
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your 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.

Shellability of semigroup rings
Available formats
×

Save article to Dropbox

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

Shellability of semigroup rings
Available formats
×

Save article to Google Drive

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

Shellability of semigroup rings
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *