starting page on possibly trivial fields, in which the trivial ring is included in the notion of field

Anonymous

]]>starting page on possibly trivial integral domains, in which the trivial ring is included in the notion of integral domain

Anonymous

]]>Created:

Lyle Eugene Pursell was a mathematician at the University of Missouri at Rolla (currently known as Missouri University of Science and Technology).

He got his PhD in 1952 from Purdue University, advised by Merrill E. Shanks.

On the embedding of smooth manifolds into formal duals of R-algebras:

- Lyle Eugene Pursell,
*Algebraic structures associated with smooth manifolds*, PhD dissertation, Purdue University, 1952. 93 pp. ISBN: 978-1392-88143-9. PDF.

!redirects Lyle Pursell !redirects Lyle E. Pursell !redirects L. Pursell !redirects L. E. Pursell

]]>Added:

The case of the category of smooth manifolds and diffeomorphisms is proved in

- Lyle Eugene Pursell,
*Algebraic structures associated with smooth manifolds*, PhD dissertation, Purdue University, 1952. 93 pp. ISBN: 978-1392-88143-9. PDF.

typo fix: morhism -> morphism

Arun Debray

]]>I don’t know if this concept already has a proper name in the commutative ring theory literature.

]]>creating article for a weaker notion of “integral domain” where the zero divisors only form an ideal instead of being equal to zero, in the same way that a local ring is where the non-invertible elements only form an ideal instead of being equal to zero.

Anonymous

]]>Add reference to Mac Lane’s “bicategories”.

]]>added section labels and a table of contents

Anonymous

]]>Thanks!

]]>also changed

“other inequality relations such as apartness relations”

to

since those are the only ones which are different from denial inequalities in constructive mathematics. General apartness relations and other irreflexive symmetric relations are still relevant in other parts of mathematics, such as local rings, even in classical mathematics.

Anonymous

]]>replaced

It is taken for granted in classical mathematics.

with

In classical mathematics, denial inequalities and tight apartness relations are the same, so the notion plays no further role classically.

Anonymous

]]>added clarfication that a Kock field is a commutative ring which satisfies Anders Kock’s Postulate K. David Jaz Myers called these objects “field in the sense of Kock” in section 4.1 of his article.

Anonymous

]]>The half-sentence

It is taken for granted in classical mathematics.

needs a little addendum: What is it that is taken for granted?

Maybe it should rather say something like this:

]]>In classical mathematics denial inequalities are just plain inequalities and so the notion plays no (further) role, classically.

I have

added specific pointer to where in David’s article this notion is considered (since a string search for “Kock field” returns empty).

added a line defining the notation”$Fin(n)$”.

started page on strictly ordered rings

Anonymous

]]>renaming page from ’linear ordered rings’ to ’linear ordered ring’

Anonymous

]]>added redirects

Anonymous

]]>starting page on linearly ordered rings

Anonymous

]]>added redirects

Anonymous

]]>added redirects

Anonymous

]]>starting disambiguation page for ordered rings

Anonymous

]]>renaming this to partially ordered ring since it is the term more commonly used in the literature.

Anonymous

]]>starting article on strict orders

Anonymous

]]>