July 1979 China and the United States signed a three-year trade agreement in Beijing, which grants each other the status of most favored nation. September 1980 The two countries signed their first textile trade agreem...July 1979 China and the United States signed a three-year trade agreement in Beijing, which grants each other the status of most favored nation. September 1980 The two countries signed their first textile trade agreement September 1983 Frictions over textile trade were resolved by a second textile trade agreement.展开更多
Recall that the semigroups S and R are said to be strongly Morita equivalent if there exists a unitary Morita context （S,R,<sub>S</sub>P<sub>R</sub>,<sub>R</sub>Q<sub>S</s...Recall that the semigroups S and R are said to be strongly Morita equivalent if there exists a unitary Morita context （S,R,<sub>S</sub>P<sub>R</sub>,<sub>R</sub>Q<sub>S</sub>,） with and surjective.For a factorisable semigroup S,we denote ζ<sub>S</sub>={（s<sub>1</sub>,s<sub>2</sub>）∈S×S|ss<sub>1</sub>=ss<sub>2</sub>,<sub>S</sub>∈S},S′=S/ζ<sub>S</sub> and US-FAct={<sub>S</sub>M∈ S-Act|SM=M and SHom<sub>S</sub>（S,M）≌M}.We show that,for factorisable semigroups S and R,the categories US-FAct and UR-FAct are equivalent if and only if the semigroups S′ and R′ are strongly Morita equivalent.Some conditions for a factorisable semigroup to be strongly Morita equivalent to a sandwich semigroup,local units semigroup,monoid and group separately are also given.Moreover,we show that a seinigroup S is completely simple if and only if S is strongly Morita equivalent to a group and for any index set I,SSHom<sub>S</sub>(S,<sub>i∈I</sub>S)→<sub>i∈I</sub>S,st·f（st）f is an S-isomorphism.展开更多
文摘July 1979 China and the United States signed a three-year trade agreement in Beijing, which grants each other the status of most favored nation. September 1980 The two countries signed their first textile trade agreement September 1983 Frictions over textile trade were resolved by a second textile trade agreement.
基金The research is partially supported by a UGC(HK) grant ≠2160092Project is supported by the National Natural Science Foundation of China
文摘Recall that the semigroups S and R are said to be strongly Morita equivalent if there exists a unitary Morita context （S,R,<sub>S</sub>P<sub>R</sub>,<sub>R</sub>Q<sub>S</sub>,） with and surjective.For a factorisable semigroup S,we denote ζ<sub>S</sub>={（s<sub>1</sub>,s<sub>2</sub>）∈S×S|ss<sub>1</sub>=ss<sub>2</sub>,<sub>S</sub>∈S},S′=S/ζ<sub>S</sub> and US-FAct={<sub>S</sub>M∈ S-Act|SM=M and SHom<sub>S</sub>（S,M）≌M}.We show that,for factorisable semigroups S and R,the categories US-FAct and UR-FAct are equivalent if and only if the semigroups S′ and R′ are strongly Morita equivalent.Some conditions for a factorisable semigroup to be strongly Morita equivalent to a sandwich semigroup,local units semigroup,monoid and group separately are also given.Moreover,we show that a seinigroup S is completely simple if and only if S is strongly Morita equivalent to a group and for any index set I,SSHom<sub>S</sub>(S,<sub>i∈I</sub>S)→<sub>i∈I</sub>S,st·f（st）f is an S-isomorphism.
