its so exciting to resume group theoretic study again that I couldnt init studying yet with cheer for reinitiation of getting expert in group theoretic topics (some chapters not all). 


(to be a better algebra representor for translatring paragraphs. e.g.. I want to learn how they represent geometry with rings. and might improvise fromt hat also for some of translations) 


(hey its not ring as usual definition of ring when talking of rings topic in blog e.g. not ornaments alike ring, its mathematical ring when were talking of modules rings. its when fields have both a summation and multiplication alike operator as far as I remember and attain associativity and distributivity properties for summation and multiplication over summation operatyor, and when tehre is 0 for summation operator and having group property for regarding summation  (but not necessarily 1 for multiplication operator nor multiplicative inverses) then its called rings as far as I remember. 

I would recheck main definition


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