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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access March 1, 2007

On homological classification of pomonoids by regular weak injectivity properties of S-posets

  • Xia Zhang EMAIL logo and Valdis Laan
From the journal Open Mathematics


If S is a partially ordered monoid then a right S-poset is a poset A on which S acts from the right in such a way that the action is compatible both with the order of S and A. By regular weak injectivity properties we mean injectivity properties with respect to all regular monomorphisms (not all monomorphisms) from different types of right ideals of S to S. We give an alternative description of such properties which uses systems of equations. Using these properties we prove several so-called homological classification results which generalize the corresponding results for (unordered) acts over (unordered) monoids proved by Victoria Gould in the 1980’s.

MSC: 06F05; 20M30

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Published Online: 2007-3-1
Published in Print: 2007-3-1

© 2007 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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