Wei Chen, Department of Mathematics, Northwest University Xi'an, Shaanxi 710069, China, e-mail: chenwei6808467@126.com; Xianzhong Zhao, Department of Mathematics, Northwest University, Xi'an, Shaanxi 710069, China, e-mail: xianzhongzhao@263.net
Abstract: In this paper we study some special residuated lattices, namely, idempotent residuated chains. After giving some properties of Green's relation $\mathcal{D}$ on the monoid reduct of an idempotent residuated chain, we establish a structure theorem for idempotent residuated chains. As an application, we give necessary and sufficient conditions for a band with an identity to be the monoid reduct of some idempotent residuated chain. Finally, based on the structure theorem for idempotent residuated chains, we obtain some characterizations of subdirectly irreducible, simple and strictly simple idempotent residuated chains.
Keywords: idempotent residuated lattice, chain, band
Classification (MSC 2000): 06F05, 20M10
Full text available as PDF (smallest), as compressed PostScript (.ps.gz) or as raw PostScript (.ps).
Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade.
To activate your access, please contact Myris Trade at myris@myris.cz.
Subscribers of Springer need to access the articles on their site, which is http://www.springeronline.com/10587.
