On the Structure of Finite Integral Commutative Residuated Chains

0365295 - ÚI 2012 RIV GB eng J - Journal Article
Horčík, Rostislav
On the Structure of Finite Integral Commutative Residuated Chains.
Journal of Logic and Computation. Roč. 21, č. 5 (2011), s. 717-728. ISSN 0955-792X. E-ISSN 1465-363X
Institutional research plan: CEZ:AV0Z10300504
Keywords : residuated lattice * ordered residuated monoid * nucleus * conucleus,Abelian lattice-ordered group * free commutative monoid
Subject RIV: BA - General Mathematics
Impact factor: 0.611, year: 2011

Among the class of finite integral commutative residuated chains (ICRCs), we identify those algebras which can be obtained as a nuclear retraction of a conuclear contraction of a totally ordered Abelian ℓ-group. We call the ICRCs satisfying this condition regular. Then we discuss the structure of finite regular ICRCs. Finally, we prove that the class of regular members generate a strictly smaller variety than the variety generated by ICRCs.
Permanent Link: http://hdl.handle.net/11104/0200571