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Prelinear Algebras in Relatively Regular Quasivarieties

机译:相对正则拟变数中的预线性代数

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摘要

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 ≤ i(x, y) (↔) x ≤ 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~--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.
机译:给定格序代数的准性,其中的线性序代数产生预线性代数的次准性。在存在常数1和二元项i的情况下,准度满足:1≤i(x,y)(↔)x≤y,我们给出了线性预准度相对于原始准度的显式公理化。具有上述属性的1和i的存在等同于准度为“相对1〜-正则”,这意味着每个相对同余均以其1类的负锥为特征。正圆锥情况下有双重结果。

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