Results 11 to 20 of about 5,949,590 (289)
Formalized Mathematics, 2021 Summary In this article we further develop field theory in Mizar [1], [2], [3] towards splitting fields. We deal with algebraic extensions [4], [5]: a field extension E of a field F is algebraic, if every element of E is algebraic over F.
Schwarzweller, Christoph +1 more
openaire +2 more sources
, 2016 The specificity of knowledge that Gene Ontology (GO) annotations currently can represent is still restricted by the legacy format of the GO annotation file, a format intentionally designed for simplicity to keep the barriers to entry low and thus encourage initial adoption.
Huntley, Rachael P. H, Lovering, Ruth C.
openaire +4 more sources
Formalized Mathematics, 2021 Summary In this article we further develop field theory [6], [7], [12] in Mizar [1], [2], [3]: we deal with quadratic polynomials and quadratic extensions [5], [4]. First we introduce quadratic polynomials, their discriminants and prove the midnight formula. Then we show that - in case the discriminant of p being non square - adjoining a
Schwarzweller, Christoph +1 more
openaire +3 more sources
Topological frame extension [PDF]
, 2013 The concept of nearness on a set was introduced by H. Herrlich. D. Le- seberg generalized nearness by introducing supernearness, which generalizes also supertopology as de ned by D. Doitchinov.
Leseberg , Dieter, Vaziry, Zohref
core +1 more source
Formalized Mathematics, 2023 Summary In this article we continue the formalization of field theory in Mizar [1], [2], [4], [3]. We introduce normal extensions: an (algebraic) extension E of F is normal if every polynomial of F that has a root in E already splits in E.
openaire +2 more sources
Transactions of the American Mathematical Society, 1980 We develop a natural five term exact sequence relating the second and third cohomology of groups. We show that this sequence is the proper framework for the problem of realizing an abstract kernel. As an application, we give an interpretation of the third cohomology of a group in terms of crossed sequences.
openaire +2 more sources
Space-time symplectic extension [PDF]
, 2001 It is conjectured that in the origin of space-time there lies a symplectic rather than metric structure. The complex symplectic symmetry Sp(2l,C), l\ge1 instead of the pseudo-orthogonal one SO(1,d-1), d\ge4 is proposed as the space-time local structure ...
F. J. Yndurain +7 more
core +3 more sources
On Extension Of Functors [PDF]
, 2011 A.Chigogidze defined for each normal functor on the category Comp an extension which is a normal functor on the category Tych. We consider this extension for any functor on the category Comp and investigate which properties it preserves from the ...
Karchevska, Lesya, Radul, Taras
core +2 more sources
Formalized Mathematics, 2023 Summary In this article we continue the formalization of field theory in Mizar. We introduce simple extensions: an extension E of F is simple if E is generated over F by a single element of E, that is E = F (a) for some a ∈ E. First, we prove that a finite extension E of F is simple if and only if there are only finitely many ...
Christoph Schwarzweller +1 more
openaire +3 more sources
ILR Labor Advance, Spring 2009 [PDF]
, 2009 ILRexNewsletter_spring2009final.pdf: 401 downloads, before Oct.
ILR Extension Labor Programs
core +1 more source