Injective Hulls are Completions of Ordered Algebras

被引：1

作者：

Zhang, Xia ^{[1
]}

Laan, Valdis ^{[2
]}

Feng, Jianjun ^{[1
]}

机构：

[1] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Peoples R China

[2] Univ Tartu, Inst Math & Stat, EE-51009 Tartu, Estonia

来源：

ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS | 2024年 / 41卷 / 02期

关键词：

Ordered algebra; Sup-algebra; Nucleus; Join-completion; Dedekind-MacNeille completion; Reflector; Linear function;

D O I：

10.1007/s11083-023-09645-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is well-known that the Dedekind-MacNeille completion of a poset is its injective hull. We prove that the injective hull of an ordered universal algebra with respect to a specific class of monomorphisms has properties that are similar to the properties of the Dedekind-MacNeille completion of a poset. In particular, this injective hull induces a reflector functor from the category of ordered algebras and continuous morphisms to the category of sup-algebras.

引用

页码：539 / 550

页数：12

共 21 条

[1] Adamek J., 1990, ABSTRACT CONCRETE CA
[2] CATEGORICAL CHARACTERIZATION OF MACNEILLE COMPLETION
BANASCHEWSKI, B
BRUNS, G
[J]. ARCHIV DER MATHEMATIK, 1967, 18 (04) : 369 - +
[3] Bishop A., 1978, Algebra Universalis, V8, P349, DOI [10.1007/BF02485405, DOI 10.1007/BF02485405]
[4] VARIETIES OF ORDERED ALGEBRAS
BLOOM, SL
[J]. JOURNAL OF COMPUTER AND SYSTEM SCIENCES, 1976, 13 (02) : 200 - 212
[5] INJECTIVE HULLS OF SEMILATTICES
BRUNS, G
LAKSER, H
[J]. CANADIAN MATHEMATICAL BULLETIN, 1970, 13 (01): : 115 - &
[6] Davey B. A., 2002, Introduction to lattices and order
[7] Erne, 1983, CONTRIBUTIONS GENERA, V2, P77
[8] THE DEDEKIND-MACNEILLE COMPLETION AS A REFLECTOR
ERNE, M
[J]. ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 1991, 8 (02): : 159 - 173
[9] ERNE M, 1987, SEMIGROUP FORUM, V34, P253
[10] Erne M., 1990, P INT S SEM THEOR IT, P63

← 1 2 3 →