Details
| Original language | English |
|---|---|
| Pages (from-to) | 115-144 |
| Number of pages | 30 |
| Journal | Applied categorical structures |
| Volume | 8 |
| Issue number | 1-2 |
| Publication status | Published - Jun 2000 |
| Event | BB Fest 96: a Conference Held at the University of Cape Town - Cape Town, South Africa Duration: 15 Jul 1996 → 20 Jul 1996 |
Abstract
We introduce ideals, radicals and prime ideals in arbitrary algebras with at least one binary operation, and we show that various separation lemmas and prime ideal theorems are special instances of one general theorem which, in turn, is equivalent to the Boolean Prime Ideal Theorem (or Ultrafilter Principle).
Keywords
- Closure system, cm-lattice, Distributive, Ideal, Locale, Prime, Quantale, Radical, Residuated, Semiprime
ASJC Scopus subject areas
- Mathematics(all)
- Theoretical Computer Science
- Computer Science(all)
- General Computer Science
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In: Applied categorical structures, Vol. 8, No. 1-2, 06.2000, p. 115-144.
Research output: Contribution to journal › Conference article › Research › peer review
}
TY - JOUR
T1 - Prime Ideal Theory for General Algebras
T2 - BB Fest 96
AU - Erné, Marcel
PY - 2000/6
Y1 - 2000/6
N2 - We introduce ideals, radicals and prime ideals in arbitrary algebras with at least one binary operation, and we show that various separation lemmas and prime ideal theorems are special instances of one general theorem which, in turn, is equivalent to the Boolean Prime Ideal Theorem (or Ultrafilter Principle).
AB - We introduce ideals, radicals and prime ideals in arbitrary algebras with at least one binary operation, and we show that various separation lemmas and prime ideal theorems are special instances of one general theorem which, in turn, is equivalent to the Boolean Prime Ideal Theorem (or Ultrafilter Principle).
KW - Closure system
KW - cm-lattice
KW - Distributive
KW - Ideal
KW - Locale
KW - Prime
KW - Quantale
KW - Radical
KW - Residuated
KW - Semiprime
UR - http://www.scopus.com/inward/record.url?scp=0042186851&partnerID=8YFLogxK
U2 - 10.1023/a:1008611926427
DO - 10.1023/a:1008611926427
M3 - Conference article
AN - SCOPUS:0042186851
VL - 8
SP - 115
EP - 144
JO - Applied categorical structures
JF - Applied categorical structures
SN - 0927-2852
IS - 1-2
Y2 - 15 July 1996 through 20 July 1996
ER -