We shall prove that f1=x2+y2+7z2 represents all eligible numbers congruent to 2 mod 3 except 14×72k which was conjectured by Kanplansky. Our method is to use modular forms of weight 3/2. Our method can also be ap...We shall prove that f1=x2+y2+7z2 represents all eligible numbers congruent to 2 mod 3 except 14×72k which was conjectured by Kanplansky. Our method is to use modular forms of weight 3/2. Our method can also be applied to other ternary quadratic forms.展开更多
We are interested in studying when the class of local modules is Baer- Kaplansky. We provide an example showing that even over a commutative semisimple ring R, we can find two non-isomorphic simple R-modules S1 and S2...We are interested in studying when the class of local modules is Baer- Kaplansky. We provide an example showing that even over a commutative semisimple ring R, we can find two non-isomorphic simple R-modules S1 and S2 such that the rings EndR（S1） and EndR（S2） are isomorphic. We show that over any ring R, the class of semisimple R-modules is Baer Kaplansky if and only if so is the class of simple R-modules.展开更多
基金the National Natural Science Foundation of China ( Grant No. 19871017).
文摘We shall prove that f1=x2+y2+7z2 represents all eligible numbers congruent to 2 mod 3 except 14×72k which was conjectured by Kanplansky. Our method is to use modular forms of weight 3/2. Our method can also be applied to other ternary quadratic forms.
文摘We are interested in studying when the class of local modules is Baer- Kaplansky. We provide an example showing that even over a commutative semisimple ring R, we can find two non-isomorphic simple R-modules S1 and S2 such that the rings EndR（S1） and EndR（S2） are isomorphic. We show that over any ring R, the class of semisimple R-modules is Baer Kaplansky if and only if so is the class of simple R-modules.
