On the finite embeddability property for residuated ordered groupoids
On the finite embeddability property for residuated ordered groupoids
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剩余有序群胚的有限可嵌入性
DOI：
10.1090/s0002-9947-04-03654-2
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
C. J. Alten
中科院分区：
文献类型：
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作者：
W. Blok;C. J. Alten
W. J. Blok和C.货车阿尔滕在2002年。利用Higman关于整除序的有限基定理，我们证明了不需要交换性和结合性的假设：整剩余序幺半群和整剩余序群胚类也有FEP。这同样适用于它们各自的（有界）（半）格序结构的子类。一般不能放弃完整性的假设-交换剩余格序幺半群类不具有FEP-但n-幂交换剩余格序幺半群类具有FEP，对于任何n
The finite embeddability property (FEP) for integral, commutative residuated ordered monoids was established by W. J. Blok and C. J. van Alten in 2002. Using Higman's finite basis theorem for divisibility orders we prove that the assumptions of commutativity and associativity are not required: the classes of integral residuated ordered monoids and integral residuated ordered groupoids have the FEP as well. The same holds for their respective subclasses of (bounded) (semi-)lattice ordered structures. The assumption of integrality cannot be dropped in general-the class of commutative, residuated, lattice ordered monoids does not have the FEP-but the class of n-potent commutative residuated lattice ordered monoids does have the FEP, for any n