Modules that are Invariant with Respect to Automorphisms and Idempotent Endomorphisms of Their Hulls and Covers

被引:0
作者
Abyzov A.N. [1 ]
Quynh T.C. [2 ]
Tuganbaev A.A. [3 ,4 ]
机构
[1] Kazan (Volga Region) Federal University, Kazan
[2] Da Nang University, Da Nang
[3] Moscow Power Engineering Institute (National Research University), Moscow
[4] M. V. Lomonosov Moscow State University, Moscow
关键词
16D40; 16D50; 16W20; automorphism-coinvariant module; automorphism-invariant module; automorphism-liftable module; cover; hull; quasi-injective module; quasi-projective module;
D O I
10.1007/s10958-021-05427-x
中图分类号
学科分类号
摘要
The paper contains both known and new results on automorphism-invariant modules, automorphism-coinvariant modules and modules which are invariant or coinvariant with respect to idempotent endomorphisms of its hull and its cover, respectively. The main results are given with proofs. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.
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页码:235 / 277
页数:42
相关论文
共 67 条
[1]  
Abyzov A.N., Le V.T., Truong C.Q., Tuganbaev A.A., Modules coinvariant under idempotent endomorphisms of their covers, Sib. Mat. Zh., 60, 6, pp. 1191-1208, (2019)
[2]  
Abyzov A.N., Quynh T.C., Tai D.D., Automorphism-invariant modules over perfect rings, Sib. Math. Zh., 58, 5, pp. 959-971, (2017)
[3]  
Alahmadi A., Er N., Jain S.K., Modules which are invariant under monomorphisms of their injective hulls, J. Austr. Math. Soc., 79, 3, pp. 349-360, (2005)
[4]  
Birkenmeier G.F., Park J.K., Rizvi S.T., Extensions of Rings and Modules, (2013)
[5]  
Camillo V.P., Khurana D., Lam T.Y., Nicholson W.K., Zhou Y., Continuous modules are clean, J. Algebra, 304, 1, pp. 94-111, (2006)
[6]  
Clark J., Lomp C., Vanaj N., Wisbauer R., Lifting Modules: Supplements and Projectivity in Module Theory, (2006)
[7]  
Dickson S.E., Fuller K.R., Algebras for which every indecomposable right module is invariant in its injective envelope, Pac. J. Math., 31, 3, pp. 655-658, (1969)
[8]  
Dinh H.Q., A note on pseudo-injective modules, Commun. Algebra, 33, pp. 361-369, (2005)
[9]  
Dung N.V., Huynh D.V., Smith P.F., Wisbauer R., Extending Modules, (1994)
[10]  
Enochs E.E., Jenda O.M.G., Relative Homological Algebra, (2011)