List questions from principal-ideal-domains

Published on 09 Jun 2019 - 10:57

60

Views

show that a kernel is principal, here the application : $ \text{ev}_{x = t^2, y = t^3} $

Published on 13 Jun 2019 - 9:12

115

Views

Surjective Map between UFD and PID

Published on 25 Mar 2026 - 12:13

87

Views

I don't understand a step in the statement of the structure theorem of finitely generated modules over a PID

Published on 25 Mar 2026 - 11:54

330

Views

Free submodule of finite index over pid

Published on 27 Mar 2026 - 6:56

35

Views

Question about isomorphism of direct sums (Step needed to show uniqueness of Elementary Divisors Theorem)

Published on 25 Mar 2026 - 11:16

176

Views

Quotient by powers of prime in a principal ideal domain

Published on 08 Jul 2019 - 13:53

167

Views

Semigroup structure of principal ideals (under products) in a Dedekind domain

Published on 25 Mar 2026 - 9:28

52

Views

A question about proof (-Module over a PID)

Published on 21 Jul 2019 - 13:51

341

Views

If R is a semilocal Dedekind domain, then R is a PID.

Published on 25 Mar 2026 - 11:16

461

Views

Find all discrete valuation subrings of $k(x)$

Published on 25 Mar 2026 - 13:55

760

Views

Find the kernel of a ring homomorphism $f(x)\to f(\sqrt 2)$

Published on 13 Aug 2019 - 7:51

402

Views

Module over PID is isomorphic to the direct sum of a submodule and the kernel of a module homomorphism

Published on 17 Aug 2019 - 21:15

94

Views

PID with countably infinitely many prime ideals and no embedding into algebraic rationals

Published on 19 Aug 2019 - 12:44

162

Views

A PID with countably infinitely many prime ideals and no embedding into complex numbers

Published on 19 Aug 2019 - 13:29

List Question

If $R[x]$ is a PID, $R$ necessarily has to be a field?

show that a kernel is principal, here the application : $ \text{ev}_{x = t^2, y = t^3} $

Surjective Map between UFD and PID

I don't understand a step in the statement of the structure theorem of finitely generated modules over a PID

Free submodule of finite index over pid

Question about isomorphism of direct sums (Step needed to show uniqueness of Elementary Divisors Theorem)

Quotient by powers of prime in a principal ideal domain

Semigroup structure of principal ideals (under products) in a Dedekind domain

A question about proof (-Module over a PID)

If R is a semilocal Dedekind domain, then R is a PID.

Find all discrete valuation subrings of $k(x)$

Find the kernel of a ring homomorphism $f(x)\to f(\sqrt 2)$

Module over PID is isomorphic to the direct sum of a submodule and the kernel of a module homomorphism

PID with countably infinitely many prime ideals and no embedding into algebraic rationals

A PID with countably infinitely many prime ideals and no embedding into complex numbers

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