S-Lattice Congruences of S-Lattices

2012 ◽  
Vol 19 (03) ◽  
pp. 465-472
Author(s):  
Congwen Luo
Keyword(s):  
Distributive Lattice ◽  
Lattice Congruence ◽  
Ordered Semigroups

In this paper, the S-lattices are introduced as a representation of lattice-ordered monoids. The smallest S-lattice congruence induced by a relation on an S-lattice is characterized and the correspondence between the S-lattice congruences and S-ideals in an S-distributive lattice is discussed. These generalize some recent results of lattices and lattice-ordered semigroups.

The Wire-Speed Multicast Switch Fabric Based on Distributive Lattice

2014 ◽  
Vol E97.B (7) ◽  
pp. 1385-1394 ◽  
Author(s):  
Fuxing CHEN ◽  
Weiyang LIU ◽  
Hui LI ◽  
Dongcheng WU
Keyword(s):  
Distributive Lattice ◽  
Switch Fabric ◽  
The Wire

Congruence relations on almost distributive lattices-II

2019 ◽  
pp. 2150005
Author(s):  
Gezahagne Mulat Addis
Keyword(s):  
Distributive Lattice ◽  
Congruence Relation ◽  
Congruence Class ◽  
Distributive Lattices ◽  
Ideal Formula ◽  
Congruence Relations

For a given ideal [Formula: see text] of an almost distributive lattice [Formula: see text], we study the smallest and the largest congruence relation on [Formula: see text] having [Formula: see text] as a congruence class.

scholarly journals Subdirect products of semirings

2001 ◽  
Vol 26 (9) ◽  
pp. 539-545
Author(s):  
P. Mukhopadhyay
Keyword(s):  
Distributive Lattice ◽  
Subdirect Product ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Subdirect Products ◽  
Necessary And Sufficient

Bandelt and Petrich (1982) proved that an inversive semiringSis a subdirect product of a distributive lattice and a ring if and only ifSsatisfies certain conditions. The aim of this paper is to obtain a generalized version of this result. The main purpose of this paper however, is to investigate, what new necessary and sufficient conditions need we impose on an inversive semiring, so that, in its aforesaid representation as a subdirect product, the “ring” involved can be gradually enriched to a “field.” Finally, we provide a construction of fullE-inversive semirings, which are subdirect products of a semilattice and a ring.

A novel study on fuzzy ideals and fuzzy filters of ordered *-semigroups

2017 ◽  
Vol 33 (1) ◽  
pp. 423-431
Author(s):  
Xinyang Feng ◽  
Jian Tang ◽  
Bijan Davvaz ◽  
Yanfeng Luo
Keyword(s):  
Ordered Semigroups ◽  
Fuzzy Filters
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