Prelinear Algebras in Relatively Regular Quasivarieties

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• 作者：C. J. van Alten (1)
  
• 关键词：Lattice ; ordered algebra ; Prelinear ; Quasivariety ; Relatively 1?regular ; 06F99 ; 03G10 ; 08C15
• 刊名：Order
• 出版年：2013
• 出版时间：July 2013
• 年：2013
• 卷：30
• 期：2
• 页码：573-583
• 全文大小：326KB
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• 作者单位：C. J. van Alten (1)
  
  1. School of Computer Science, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050, Johannesburg, South Africa
  
• ISSN：1572-9273

文摘

Given a quasivariety of lattice-ordered algebras, the linearly ordered algebras therein generate the subquasivariety of prelinear algebras. In the case that there exist a constant 1 and binary term i such that the quasivariety satisfies: $1 \leq i(x,y) \Leftrightarrow x \leq y$ , we give an explicit axiomatization of the prelinear subquasivariety, relative to the original quasivariety. The existence of 1 and i with the above property is equivalent to the quasivariety being ‘relatively 1?/sup>-regular- by which we mean that each relative congruence is characterized by the negative cone of its 1-class. Dual results hold in the positive cone case.