×
Abyzov, Adel; Tien Dat, Bui; Quynh, Truong Cong

Small dual-AdS modules, small AdS\(^\sharp\) and small AdS\(^\ast\) modules. (English) Zbl 1542.16004

Lobachevskii J. Math. 44, No. 12, 5097-5115 (2023).

MSC:

16D70 Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)
16D40 Free, projective, and flat modules and ideals in associative algebras
16D50 Injective modules, self-injective associative rings
16D80 Other classes of modules and ideals in associative algebras

Keywords:

AdS modules; AdS\(^\ast\) modules; small self-projective modules
Cite Review PDF
Full Text: DOI

References:

[1] A. N. Abyzov, T. C. Quynh, N. T. T. Ha, and T. Yildirim, ‘‘Modules close to the automorphism invariant and coinvariant,’’ J. Algebra Appl. 18, 1950235 (2019). · Zbl 1430.16005
[2] Abyzov, A. N.; Quynh, T. C., Lifting of automorphisms of factor modules, Commun. Algebra, 46, 5073-5082, 2018 · Zbl 1400.16005 · doi:10.1080/00927872.2018.1461884
[3] Alahmadi, A.; Jain, S. K.; Leroy, A., ADS modules, J. Algebra, 352, 215-222, 2012 · Zbl 1256.16005 · doi:10.1016/j.jalgebra.2011.10.035
[4] J. Clark, C. Lomp, N. Vanaja, and R. Wisbauer, Lifting Modules: Supplements and Projectivity in Module Theory, Frontiers in Mathematics (Birkhäuser, Basel, 2006). · Zbl 1102.16001
[5] D’este, G.; Tütüncü, D. K.; Tribak, R., D3-modules versus D4-modules-Applications to quivers, Glasgo Math. J., 63, 697-723, 2021 · Zbl 1483.16002 · doi:10.1017/S0017089520000452
[6] N. Ding, Y. Ibrahim, M. Yousif, and Y. Zhou, ‘‘D4-modules,’’ J. Algebra Appl. 16, 1750166 (2017). · Zbl 1382.16003
[7] N. V. Dung, D. V. Huynh, P. F. Smith, and R. Wisbauer, Extending Modules, Vol. 313 of Pitman Research Notes in Math. (Longman, Harlow, New York, 1994). · Zbl 0841.16001
[8] Golan, J. S., Characterization of rings using quasiprojective modules, Israel J. Math., 8, 34-38, 1970 · Zbl 0199.35502 · doi:10.1007/BF02771548
[9] Guil Asensio, P. A.; Quynh, T. C.; Srivastava, A. K., Additive unit structure of endomorphism rings and invariance of modules, Bull. Math. Sci., 7, 229-246, 2017 · Zbl 1392.16004 · doi:10.1007/s13373-016-0096-z
[10] Kasch, F., Modules and Rings, 1982, New York: Academic, New York · Zbl 0523.16001
[11] Kasch, F.; Mader, A., Regularity and substructures of Hom, Commun. Algebra, 34, 1459-1478, 2006 · Zbl 1122.16005 · doi:10.1080/00927870500455031
[12] S. H. Mohammed and B. J. Müller, Continous and Discrete Modules, Vol. 147 of London Math. Soc. LN (Cambridge Univ. Press, Cambridge, 1990). · Zbl 0701.16001
[13] Nicholson, W. K.; Zhou, Y., Semiregular morphisms, Commun. Algebra, 34, 219-233, 2006 · Zbl 1148.16010 · doi:10.1080/00927870500346214
[14] Özcan, A. Ç.; Harmanci, A.; Smith, P. F., Duo modules, Glasgo Math. J., 48, 533-545, 2006 · Zbl 1116.16003 · doi:10.1017/S0017089506003260
[15] Quynh, T. C.; Koşan, M. T., On ADS modules and rings, Commun. Algebra, 42, 3541-3551, 2014 · Zbl 1301.16005 · doi:10.1080/00927872.2013.788185
[16] Quynh, T. C.; Şahinkaya, S., On dual automorphism-invariant and superfluous ADS-modules, Contemp. Math., 727, 3541-3551, 2019
[17] Singh, S.; Srivastava, A. K., Dual automorphism-invariant modules, J. Algebra, 371, 262-275, 2012 · Zbl 1276.16003 · doi:10.1016/j.jalgebra.2012.08.012
[18] Tercan, A.; Yücel, C. C., Module Theory. Extending Modules and Generalizations, 2016, Basel: Birkhäuser-Springer, Basel · Zbl 1368.16002 · doi:10.1007/978-3-0348-0952-8
[19] Trang, D. T.; Koşan, M. T.; Taşdemir, Ö.; Quynh, T. C., On modules and rings having large absolute direct summands, Commun. Algebra, 51, 4949-4961, 2023 · Zbl 1535.16001 · doi:10.1080/00927872.2023.2223301
[20] Tribak, R.; Tütüncü, D. K.; Ertaş, N. O., Direct sums of ADS* modules, Bol. Soc. Mat. Mex., 51, 33-46, 2015 · Zbl 1345.16004
[21] Tuganbaev, A. A., Automorphism-extendable and endomorphirsm-extendable modules, J. Math. Sci., 245, 234-284, 2020 · Zbl 1460.16004 · doi:10.1007/s10958-020-04689-1
[22] A. A. Tuganbaev, ‘‘Automorphism-liftable modules,’’ J. Algebra Appl. 21, 2250106 (2022). · Zbl 1523.16003
[23] Tütüncü, D. K., A note on ADS* modules, Bull. Math. Sci., 2, 359-363, 2012 · Zbl 1255.16004 · doi:10.1007/s13373-012-0020-0
[24] Wisbauer, R., Foundations of Module and Ring Theory. A Handbook for Study and Research, 1991, Reading: Gordon and Breach, Reading · Zbl 0746.16001
[25] Wu, L. E. T.; Jans, J. P., On quasi projectives, Illinois J. Math., 11, 439-448, 1967 · Zbl 0153.06301 · doi:10.1215/ijm/1256054566
[26] Yousif, M.; Amin, I.; Ibrahim, Y., D3-modules, Commun. Algebra, 42, 578-592, 2014 · Zbl 1307.16003 · doi:10.1080/00927872.2012.718823
[27] J. Xu, Flat Covers of Modules, Vol. 1634 of Lecture Notes in Mathematics (Springer, Berlin, 1996). · Zbl 0860.16002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.