What module is of finite length whose submodules aren't? [closed]











up vote
0
down vote

favorite












Does such an example exist? It seems strange that a module whose submodules have infinite length has somehow infinite length






modules







share|cite|improve this question













closed as off-topic by Zvi, Lord Shark the Unknown, Brahadeesh, KReiser, Shailesh Nov 24 at 11:28


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Zvi, Brahadeesh, KReiser, Shailesh

If this question can be reworded to fit the rules in the help center, please edit the question.

















    up vote
    0
    down vote

    favorite












    Does such an example exist? It seems strange that a module whose submodules have infinite length has somehow infinite length






    modules







    share|cite|improve this question













    closed as off-topic by Zvi, Lord Shark the Unknown, Brahadeesh, KReiser, Shailesh Nov 24 at 11:28


    This question appears to be off-topic. The users who voted to close gave this specific reason:


    • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Zvi, Brahadeesh, KReiser, Shailesh

    If this question can be reworded to fit the rules in the help center, please edit the question.















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      Does such an example exist? It seems strange that a module whose submodules have infinite length has somehow infinite length






      modules







      share|cite|improve this question













      Does such an example exist? It seems strange that a module whose submodules have infinite length has somehow infinite length






      modules




      modules






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Nov 22 at 16:47









      Ben-ZT

      1889




      1889




      closed as off-topic by Zvi, Lord Shark the Unknown, Brahadeesh, KReiser, Shailesh Nov 24 at 11:28


      This question appears to be off-topic. The users who voted to close gave this specific reason:


      • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Zvi, Brahadeesh, KReiser, Shailesh

      If this question can be reworded to fit the rules in the help center, please edit the question.




      closed as off-topic by Zvi, Lord Shark the Unknown, Brahadeesh, KReiser, Shailesh Nov 24 at 11:28


      This question appears to be off-topic. The users who voted to close gave this specific reason:


      • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Zvi, Brahadeesh, KReiser, Shailesh

      If this question can be reworded to fit the rules in the help center, please edit the question.






















          1 Answer
          1






          active

          oldest

          votes

















          up vote
          1
          down vote













          Let $R$ be a ring. An $R$-module $M$ has finite length if and only if it is artinian and noetherian. Since these two properties are inherited by $R$-submodules, if $Nleq M$ is an $R$-submodule of a finite-length module $M$, $N$ is artinian and noetherian. Hence it has finite length.






          share|cite|improve this answer




























            1 Answer
            1






            active

            oldest

            votes








            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes








            up vote
            1
            down vote













            Let $R$ be a ring. An $R$-module $M$ has finite length if and only if it is artinian and noetherian. Since these two properties are inherited by $R$-submodules, if $Nleq M$ is an $R$-submodule of a finite-length module $M$, $N$ is artinian and noetherian. Hence it has finite length.






            share|cite|improve this answer

























              up vote
              1
              down vote













              Let $R$ be a ring. An $R$-module $M$ has finite length if and only if it is artinian and noetherian. Since these two properties are inherited by $R$-submodules, if $Nleq M$ is an $R$-submodule of a finite-length module $M$, $N$ is artinian and noetherian. Hence it has finite length.






              share|cite|improve this answer























                up vote
                1
                down vote










                up vote
                1
                down vote









                Let $R$ be a ring. An $R$-module $M$ has finite length if and only if it is artinian and noetherian. Since these two properties are inherited by $R$-submodules, if $Nleq M$ is an $R$-submodule of a finite-length module $M$, $N$ is artinian and noetherian. Hence it has finite length.






                share|cite|improve this answer












                Let $R$ be a ring. An $R$-module $M$ has finite length if and only if it is artinian and noetherian. Since these two properties are inherited by $R$-submodules, if $Nleq M$ is an $R$-submodule of a finite-length module $M$, $N$ is artinian and noetherian. Hence it has finite length.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Nov 23 at 7:18









                Blumer

                438110




                438110















                    -

                    Popular posts from this blog

                    Quarter-circle Tiles

                    Image
                    up vote 0 down vote favorite I have $99$ identical square tiles, each with a quarter-circle drawn on it like this: [asy] size(1.5cm); draw(Arc((2,0),1,90,180),red+1); draw((0,0)--(2,0)--(2,2)--(0,2)--(0,0)); [/asy] When I arrange the tiles in a $9times 11$ rectangular grid, each with a random orientation, what is the expected value of the number of full circles I form? I think this problem has to do with finding the chance any given 2x2 square has a circle, but I can't find it. expected-value share | cite | improve this question asked Nov 20 at 15:03 6minecraftninja 1 2
                    Read more

                    build a pushdown automaton that recognizes the reverse language of a given pushdown automaton?

                    Image
                    0 I think it's similiar to NFAs. I replace the finite states of the given automaton for start-states for my new automaton. I do it with $epsilon$ -transition from the start state to the actual finite states of the given automaton. The start state of the given automaton will be my accepting(finite) state of my new one. All transitions will be reversed of course to recognize the reversed word. But how do I have to change the stack of the pushdown automaton? That's tricky. formal-languages automata context-free-grammar share | cite | improve this question edited Nov 29 '18 at 14:20 joee
                    Read more

                    Mont Emei

                    Image
                    Mont Emei.mw-parser-output .entete.map{background-image:url("//upload.wikimedia.org/wikipedia/commons/7/7a/Picto_infobox_map.png")} Vue du sommet Wanfo du mont Emei Géographie Altitude 3 099  m , Wanfo Coordonnées 29° 31′ 11″ nord, 103° 19′ 57″ est Administration Pays   Chine Province Sichuan Ville-préfecture Leshan Géolocalisation sur la carte : Sichuan Mont Emei Géolocalisation sur la carte : Chine Mont Emei modifier   Paysage panoramique du mont Emei, incluant le paysage panoramique du grand Bouddha de Leshan *   Patrimoine mondial de l'UNESCO Passerelle en bois sur le versant ouest Pays   Chine Subdivision Sichuan Type Mixte Critères (iv) (vi) (x) Superficie 15 400 ha Numéro d’identification 779 Zone géographique Asie et Pacifique  ** Année d’inscription 1996 (20 e session) * Descriptif officiel UNESCO ** Classification géog
                    Read more