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Suppose a ring R is a PID. What does this say about possible orders on the set of R?

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#group-theory #order-theory #principal-ideal-domains #ordered-groups
285
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Being a PID is not a local property

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#algebraic-geometry #principal-ideal-domains
378
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Which principal ideal rings are homomorphic image of principal ideal domain?

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#ring-theory #commutative-algebra #ideals #principal-ideal-domains
692
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Principal ideal domain question.

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#abstract-algebra #ring-theory #principal-ideal-domains
676
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Proper Ideal is a Product of Maximal Ideals

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#abstract-algebra #ring-theory #principal-ideal-domains #unique-factorization-domains
2.6k
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Product of Primary Ideals is the Intersection of Prime Ideals

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#abstract-algebra #ring-theory #principal-ideal-domains #unique-factorization-domains
838
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Finite Number of Principal Ideals

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#abstract-algebra #ring-theory #principal-ideal-domains #unique-factorization-domains
64
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Determine if this affirmation about modules over PID are true

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#abstract-algebra #modules #ideals #principal-ideal-domains
61
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If $M,N$ D-modules, $ann(M \oplus N)=\langle c\rangle$

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#abstract-algebra #modules #principal-ideal-domains
33
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If $a=bc$ then $\langle b \rangle / \langle a \rangle \simeq D/\langle c \rangle$

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#abstract-algebra #quotient-spaces #principal-ideal-domains
78
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Non-principal ideal in a ring which is not a domain

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#abstract-algebra #ring-theory #ideals #principal-ideal-domains
697
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Show that every principal ideal domain is a unique factorisation domain

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#abstract-algebra #ring-theory #principal-ideal-domains #unique-factorization-domains
449
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A PID that is a sub ring of a Non-PID

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#abstract-algebra #ring-theory #principal-ideal-domains #unique-factorization-domains
204
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Free modules over a PID

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#abstract-algebra #exact-sequence #principal-ideal-domains #free-modules
1.1k
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Prove that a UFD $R$ is a PID if every nonzero prime ideal in $R$ is maximal.

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#ring-theory #maximal-and-prime-ideals #principal-ideal-domains #unique-factorization-domains

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