Details
| Original language | English |
|---|---|
| Pages (from-to) | 312-319 |
| Number of pages | 8 |
| Journal | Algebra universalis |
| Volume | 11 |
| Issue number | 1 |
| Publication status | Published - Dec 1980 |
Abstract
Within the theory of ideals in partially ordered sets, several difficulties set in which do not occur in the special case of lattices (or bidirected posets). For example, a finite product of ideals in the factor posets need not be an ideal in the product poset. The notion of strict ideals is introduced in order to remedy some deficiencies occurring in the general case of an arbitrary product of posets. Besides other results, we show the following main theorem: The ideal topology (cf. [2]) of a product of non-trivial posets coincides with the product topology if and only if the number of factors is finite (4.19.).
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
- Mathematics(all)
- Logic
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In: Algebra universalis, Vol. 11, No. 1, 12.1980, p. 312-319.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Topologies on products of partially ordered sets II
T2 - Ideal topologies
AU - Erné, Marcel
PY - 1980/12
Y1 - 1980/12
N2 - Within the theory of ideals in partially ordered sets, several difficulties set in which do not occur in the special case of lattices (or bidirected posets). For example, a finite product of ideals in the factor posets need not be an ideal in the product poset. The notion of strict ideals is introduced in order to remedy some deficiencies occurring in the general case of an arbitrary product of posets. Besides other results, we show the following main theorem: The ideal topology (cf. [2]) of a product of non-trivial posets coincides with the product topology if and only if the number of factors is finite (4.19.).
AB - Within the theory of ideals in partially ordered sets, several difficulties set in which do not occur in the special case of lattices (or bidirected posets). For example, a finite product of ideals in the factor posets need not be an ideal in the product poset. The notion of strict ideals is introduced in order to remedy some deficiencies occurring in the general case of an arbitrary product of posets. Besides other results, we show the following main theorem: The ideal topology (cf. [2]) of a product of non-trivial posets coincides with the product topology if and only if the number of factors is finite (4.19.).
UR - http://www.scopus.com/inward/record.url?scp=51649161134&partnerID=8YFLogxK
U2 - 10.1007/BF02483110
DO - 10.1007/BF02483110
M3 - Article
AN - SCOPUS:51649161134
VL - 11
SP - 312
EP - 319
JO - Algebra universalis
JF - Algebra universalis
SN - 0002-5240
IS - 1
ER -