Algebraic Structures that are similar to Vector Spaces but exist over a Commutative Ring as opposed to a Field?

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I was just wondering if there are Vector Space 'like' structures in which instead of existing over a Field exist over a Commutative Ring?



Thanks, David




abstract-algebra ring-theory vector-spaces field-theory




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    You're welcome $$textrm$$ -David
    – D_S
    Aug 1 at 2:33















up vote
1
down vote

favorite












I was just wondering if there are Vector Space 'like' structures in which instead of existing over a Field exist over a Commutative Ring?



Thanks, David




abstract-algebra ring-theory vector-spaces field-theory




share|cite|improve this question















  • 2




    You're welcome $$textrm$$ -David
    – D_S
    Aug 1 at 2:33













up vote
1
down vote

favorite









up vote
1
down vote

favorite











I was just wondering if there are Vector Space 'like' structures in which instead of existing over a Field exist over a Commutative Ring?



Thanks, David




abstract-algebra ring-theory vector-spaces field-theory




share|cite|improve this question











I was just wondering if there are Vector Space 'like' structures in which instead of existing over a Field exist over a Commutative Ring?



Thanks, David





abstract-algebra ring-theory vector-spaces field-theory





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Aug 1 at 1:24









user3053801

1008




1008







  • 2




    You're welcome $$textrm$$ -David
    – D_S
    Aug 1 at 2:33













  • 2




    You're welcome $$textrm$$ -David
    – D_S
    Aug 1 at 2:33








2




2




You're welcome $$textrm$$ -David
– D_S
Aug 1 at 2:33





You're welcome $$textrm$$ -David
– D_S
Aug 1 at 2:33











1 Answer
1






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2
down vote



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There exists the notion of a module over a ring, see http://mathworld.wolfram.com/Module.html.






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  • Thanks @Matt. Much appreciated.
    – user3053801
    Aug 1 at 1:27






  • 1




    No problem! I hope this helps.
    – Matt
    Aug 1 at 1:28






  • 1




    The field that covers the study of modules over commutative rings is called commutative algebra.
    – Thomas Andrews
    Aug 1 at 1:47










  • @ThomasAndrews - Thanks for that :-)
    – user3053801
    Aug 1 at 3:17










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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
2
down vote



accepted










There exists the notion of a module over a ring, see http://mathworld.wolfram.com/Module.html.






share|cite|improve this answer





















  • Thanks @Matt. Much appreciated.
    – user3053801
    Aug 1 at 1:27






  • 1




    No problem! I hope this helps.
    – Matt
    Aug 1 at 1:28






  • 1




    The field that covers the study of modules over commutative rings is called commutative algebra.
    – Thomas Andrews
    Aug 1 at 1:47










  • @ThomasAndrews - Thanks for that :-)
    – user3053801
    Aug 1 at 3:17














up vote
2
down vote



accepted










There exists the notion of a module over a ring, see http://mathworld.wolfram.com/Module.html.






share|cite|improve this answer





















  • Thanks @Matt. Much appreciated.
    – user3053801
    Aug 1 at 1:27






  • 1




    No problem! I hope this helps.
    – Matt
    Aug 1 at 1:28






  • 1




    The field that covers the study of modules over commutative rings is called commutative algebra.
    – Thomas Andrews
    Aug 1 at 1:47










  • @ThomasAndrews - Thanks for that :-)
    – user3053801
    Aug 1 at 3:17












up vote
2
down vote



accepted







up vote
2
down vote



accepted






There exists the notion of a module over a ring, see http://mathworld.wolfram.com/Module.html.






share|cite|improve this answer













There exists the notion of a module over a ring, see http://mathworld.wolfram.com/Module.html.







share|cite|improve this answer













share|cite|improve this answer



share|cite|improve this answer











answered Aug 1 at 1:26









Matt

1,789517




1,789517











  • Thanks @Matt. Much appreciated.
    – user3053801
    Aug 1 at 1:27






  • 1




    No problem! I hope this helps.
    – Matt
    Aug 1 at 1:28






  • 1




    The field that covers the study of modules over commutative rings is called commutative algebra.
    – Thomas Andrews
    Aug 1 at 1:47










  • @ThomasAndrews - Thanks for that :-)
    – user3053801
    Aug 1 at 3:17
















  • Thanks @Matt. Much appreciated.
    – user3053801
    Aug 1 at 1:27






  • 1




    No problem! I hope this helps.
    – Matt
    Aug 1 at 1:28






  • 1




    The field that covers the study of modules over commutative rings is called commutative algebra.
    – Thomas Andrews
    Aug 1 at 1:47










  • @ThomasAndrews - Thanks for that :-)
    – user3053801
    Aug 1 at 3:17















Thanks @Matt. Much appreciated.
– user3053801
Aug 1 at 1:27




Thanks @Matt. Much appreciated.
– user3053801
Aug 1 at 1:27




1




1




No problem! I hope this helps.
– Matt
Aug 1 at 1:28




No problem! I hope this helps.
– Matt
Aug 1 at 1:28




1




1




The field that covers the study of modules over commutative rings is called commutative algebra.
– Thomas Andrews
Aug 1 at 1:47




The field that covers the study of modules over commutative rings is called commutative algebra.
– Thomas Andrews
Aug 1 at 1:47












@ThomasAndrews - Thanks for that :-)
– user3053801
Aug 1 at 3:17




@ThomasAndrews - Thanks for that :-)
– user3053801
Aug 1 at 3:17












 

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