The notions of F I-t-lifting modules and t-quasi-dual Baer modules are introduced and the relations between them are studied in this paper.It is shown that an amply supplemented module M is an F I-t-lifting module if ...The notions of F I-t-lifting modules and t-quasi-dual Baer modules are introduced and the relations between them are studied in this paper.It is shown that an amply supplemented module M is an F I-t-lifting module if and only if every fully invariant t-coclosed submodule of M is a direct summand of M if and only if Z^(2)is a direct summand of M and Z^(2)(M)is an F I-lifting module if and only if M is t-quasi-dual Baer and an F I-t-K-module.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
We introduce the notions of IDS modules, IP modules, and Baer＊ modules, which are new generalizations of von Neumann regular rings, PP rings, and Baer rings, respectively, in a general module theoretic setting. We ob...We introduce the notions of IDS modules, IP modules, and Baer＊ modules, which are new generalizations of von Neumann regular rings, PP rings, and Baer rings, respectively, in a general module theoretic setting. We obtain some characterizations and properties of IDS modules, IP modules and Baer modules. Some important classes of rings are characterized in terms of IDS modules, IP modules, and Baer modules.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12301055)。
文摘The notions of F I-t-lifting modules and t-quasi-dual Baer modules are introduced and the relations between them are studied in this paper.It is shown that an amply supplemented module M is an F I-t-lifting module if and only if every fully invariant t-coclosed submodule of M is a direct summand of M if and only if Z^(2)is a direct summand of M and Z^(2)(M)is an F I-lifting module if and only if M is t-quasi-dual Baer and an F I-t-K-module.
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.
基金This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11171149, 11371187）, Jiangsu 333 Project, and Jiangsu Six Major Talents Peak Project.
文摘We introduce the notions of IDS modules, IP modules, and Baer＊ modules, which are new generalizations of von Neumann regular rings, PP rings, and Baer rings, respectively, in a general module theoretic setting. We obtain some characterizations and properties of IDS modules, IP modules and Baer modules. Some important classes of rings are characterized in terms of IDS modules, IP modules, and Baer modules.
