Search results

...(set theory)|union]] of any two elements of the ideal must also be in the ideal. More formally, given a set <math>X,</math> an ideal <math>I</math> on <math>X</math> is a [[Empty set|nonempty]] subset of the

...[[order theory]]). This article focuses on prime ideal theorems from order theory. ...FC) that the Boolean prime ideal theorem is often taken as an axiom of set theory. The abbreviations BPI or PIT (for Boolean algebras) are sometimes used to

{{Ring theory sidebar|Basic}} ...used to construct a [[quotient ring]] in a way similar to how, in [[group theory]], a [[normal subgroup]] can be used to construct a [[quotient group]].

{{Short description|Order whose elements are all comparable}} {{redirect-distinguish|Linear order|Linear order (linguistics)}}

{{for|filters on sets|Filter (set theory)}} ...ality (order theory)|dual]] to a filter is an [[Ideal (order theory)|order ideal]].

...Bergman | title=On lattices and their ideal lattices, and posets and their ideal posets| journal= Tbilisi Math. J. | volume= 1 |year=2008 | p= 89 | url=http * {{annotated link|Ideal (ring theory)}}

...em" redirects here. For the branch of Galois theory, see [[Artin–Schreier theory]].}} ...ld (mathematics)|field]] ''F'' that has the same [[first-order logic|first-order]] properties as the field of [[real number]]s. Some examples are the field

| title = Coloring infinite graphs and the Boolean prime ideal theorem | title = Introduction to Lattices and Order

...unders |title=Sheaves in geometry and logic: a first introduction to topos theory |date=1992 |publisher=Springer-Verlag |location=New York |isbn=978-0-387-97 | title =Prime ideal structure in commutative rings

...last1=Priest |first2=Terry |last2=Forbes |title=Magnetic Reconnection: MHD Theory and Applications |publisher=Cambridge University Press |edition=First |year ...properties of [[scalar triple product]]s and a [[Perturbation theory|first-order approximation]] was taken. Substituting this into the expression for <math>

...ी है।<ref>[[Ira H. Abbott|Abbott, Ira H.]], and Von Doenhoff, Albert E., ''Theory of Wing Sections'', Section 1.2 and Appendix IV</ref> ...flowfield, and of induced drag, but this is misleading. It is true that in order for the large-scale flow pattern of Figure 3.1 to exist, there must be a vo

...|publication-place=New York, USA |date=1962 |edition=1 |lccn=61-17340 |id=Order No. 26590 |pages=353–354 |quote-page=354 |quote=The voltage ''drop'' from ...Graw-Hill Professional]] |date=2002 |edition=4 |series=Schaum's outline of theory and problems / Schaum's outline series |isbn=0-07-139307-2 |page=338 |url=h

...ochster |first=Melvin |authorlink = Melvin Hochster|year=1969 |title=Prime ideal structure in commutative rings |publisher=Trans. Amer. Math. Soc. |volume=1 {{Order theory}}

...ch is equivalent to the [[compactness theorem]] and to the [[Boolean prime ideal theorem]]) may be used instead. Hahn-Banach can also be proved using [[Tych In [[Category theory|category-theoretic]] terms, the underlying field of the vector space is an

...efinitions are in this hidden table to keep them together, in alphabetical order and to reduce inline clutter. --> ...e used in place of an ideal transformer. One essential difference is that ideal transformers continue to work when energised with [[direct current|DC]], so

...h respect to a derivation; special polynomials may generate a differential ideal while normal polynomials are [[Square-free polynomial | squarefree]]. The * {{annotated link|Differential Galois theory}}

| title = If a polynomial identity guarantees that every partial order on a ring can be extended, then this identity is true only for a zero-ring | trans-title = Ideal theory in rings

...al theme; that of circularity." Foerster, H. von (2003). Ethics and second-order cybernetics, in Understanding understanding: Essays on cybernetics and cogn

! order <math>\Theta_n</math> ...st1 = Min Hoon | last1 = Kim | first2 = Shohei | last2 = Yamada | title = Ideal classes and Cappell-Shaneson homotopy 4-spheres | arxiv=1707.03860v1| year

...h "DN model of explanation and [[hypothetico-deductive model|HD model]] of theory development", pp 25–26.</ref> <ref name="Bechtel-axiomatic">Bechtel, ''Ph ...[epistemology|theory of knowledge]] on par with [[Newton's theory|Newton's theory of motion]] (Buckle [https://books.google.com/books?id=jiq14nexzu0C&pg=PA70