The Lattice of Subvarieties of Semilattice Ordered Algebras

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• 作者：A. Pilitowska (1)
  A. Zamojska-Dzienio (1)
  
• 关键词：Ordered structures ; Semilattices ; Power algebras ; Free algebras ; Fully invariant congruences ; Varieties ; Lattice of subvarieties ; 08B15 ; 08B20 ; 08A30 ; 06A12 ; 06F25
• 刊名：Order
• 出版年：2014
• 出版时间：July 2014
• 年：2014
• 卷：31
• 期：2
• 页码：217-238
• 全文大小：
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• 作者单位：A. Pilitowska (1)
  A. Zamojska-Dzienio (1)
  
  1. Faculty of Mathematics and Information Science, Warsaw University of Technology, ul. Koszykowa 75, 00-662, Warsaw, Poland
  
• ISSN：1572-9273

文摘

This paper is devoted to the semilattice ordered \(\mathcal{V}\) -algebras of the form (A, Ω, +-, where + is a join-semilattice operation and (A, Ω) is an algebra from some given variety \(\mathcal{V}\) . We characterize the free semilattice ordered algebras using the concept of extended power algebras. Next we apply the result to describe the lattice of subvarieties of the variety of semilattice ordered \(\mathcal{V}\) -algebras in relation to the lattice of subvarieties of the variety \(\mathcal{V}\) .