dc.contributor.author |
Kumar, Rahul |
|
dc.date.accessioned |
2023-08-17T06:18:40Z |
|
dc.date.available |
2023-08-17T06:18:40Z |
|
dc.date.issued |
2021 |
|
dc.identifier.uri |
https://pjm.ppu.edu/sites/default/files/papers/PJM_June_2021_373_382_0.pdf |
|
dc.identifier.uri |
http://dspace.bits-pilani.ac.in:8080/xmlui/handle/123456789/11466 |
|
dc.description.abstract |
This paper is a sequel. The earlier paper introduced, for any (unital) extension of (commutative
unital) rings R T, an invariant L(T=R) defined as the supremum of the lengths of chains of intermediate
fields in the extension kR(Q \ R) kT (Q), where Q runs over the prime ideals of T. Theorem 2.5 of
that earlier paper calculated L(T=R) in case R T are (commutative integral) domains such that R T
are “adjacent rings" (that is, in case R T is a minimal ring extension of domains). The statement of that
Theorem 2.5 is incorrect for some adjacent rings R T such that R is integrally closed in T. Counterexamples
are given to the original statement of Theorem 2.5. Two corrected versions of Theorem 2.5 are stated, proved
and generalized from the domain-theoretic setting to the context of extensions of arbitrary rings. These results
lead naturally to discussions involving the conductor (R : T) arising from a normal pair (R; T) of rings. |
en_US |
dc.language.iso |
en |
en_US |
dc.publisher |
Palestine Polytechnic University |
en_US |
dc.subject |
Mathematics |
en_US |
dc.subject |
Commutative ring |
en_US |
dc.subject |
Ring extension |
en_US |
dc.subject |
Minimal ring extension |
en_US |
dc.subject |
Inert extension |
en_US |
dc.subject |
Crucial maximal ideal |
en_US |
dc.subject |
Integrality |
en_US |
dc.title |
On a field-theoretic invariant for extensions of commutative rings, II |
en_US |
dc.type |
Article |
en_US |