Lattices of pseudovarieties

Journal of the Australian Mathematical Society

P. Agliano¹ 

[1] J. B. Nation

关键词: 08 B 15;    08 C 99;   

DOI  :  10.1017/S1446788700030640

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

We consider the lattice of pseudovarieties contained in a given pseudovariety P. It is shown that if the lattice L of subpseudovarieties of P has finite height, then L is isomorphic to the lattice of subvarieties of a locally finite variety. Thus not every finite lattice is isomorphic to a lattice of subpseudovarieties. Moreover, the lattice of subpseudovarieties of P satisfies every positive universal sentence holding in all lattice of subvarieties of varieties V(A) ganarated by algebras A ε P.

【 授权许可】

Unknown