On M-coidempotent elements and fully coidempotent modules

References

• Al-Shaniafi, Y., Smith, P.F. (2011). Comultiplication modules over commutative rings. J. Commut. Algebra 3(1):1–29. DOI: 10.1216/JCA-2011-3-1-1.
   Web of Science ®Google Scholar
• Al-Shaniafi, Y., Smith, P. F. (2012). Comultiplication modules over commutative rings II. J. Commut. Algebra 4(2):153–174. DOI: 10.1216/JCA-2012-4-2-153.
   Web of Science ®Google Scholar
• Anderson, W., Fuller, K. R. (1974). Rings and Categories of Modules. New York-Heidelberg-Berlin: Springer-Verlag.
   Google Scholar
• Anderson, D. D., Chun, S., Juett, J. R. (2019). Module-theoretic generalization of commutative von Neumann regular rings. Commun. Algebra 47(11):4713–4728. DOI: 10.1080/00927872.2019.1593427.
   Web of Science ®Google Scholar
• Ansari-Toroghy, H., Farshadifar, F. (2007). The dual notion of multiplication modules. Taiwanese J. Math. 11(4):1189–1201. DOI: 10.11650/twjm/1500404812.
   Web of Science ®Google Scholar
• Ansari-Toroghy, H., Farshadifar, F. (2008). Comultiplication modules and related results. Honam Math. J. 30(1):91–99. DOI: 10.5831/HMJ.2008.30.1.091.
   Google Scholar
• Ansari-Toroghy, H., Farshadifar, F. (2008). On comultiplication modules. Korean Ann. Math. 25(2):57–66.
   Google Scholar
• Ansari-Toroghy, H., Farshadifar, F. (2009). Strong comultiplication modules. CMU. J. Nat. Sci. 8(1):105–113.
   Google Scholar
• Atiyah, M. F., Macdonald, I. G. (1969). Introduction to Commutative Algebra. Reading, Mass: Addison-Wesley.
   Google Scholar
• Ansari-Toroghy, H., Farshadifar, F. (2011). The dual notions of some generalizations of prime submodules. Commun. Algebra 39(7):2396–2416. DOI: 10.1080/00927872.2010.488684.
   Web of Science ®Google Scholar
• Ansari-Toroghy, H., Farshadifar, F. (2012). Fully idempotent and coidempotent modules. Bull. Iranian Math. Soc. 38(4):987–1005.
   Web of Science ®Google Scholar
• Ansari-Toroghy, H., Farshadifar, F. (2012). On the dual notion of prime submodules II. Mediterr. J. Math. 9(2):327–336. DOI: 10.1007/s00009-011-0129-5.
   Web of Science ®Google Scholar
• Behboodi, M., Karamzadeh, O. A. S., Koohy, H. (2004). Modules whose certain submodules are prime. Vietnam J. Math. 32(3):303–317.
   Google Scholar
• Çeken, S., Alkan, M. (2011). Dual of Zariski topology for modules. Book Series: AIP Conf. Proc. 1389(1):357–360.
   Google Scholar
• Çeken, S., Alkan, M., Smith, P. F. (2013). Second modules over noncommutative rings. Commun. Algebra 41(1):83–98. DOI: 10.1080/00927872.2011.623026.
   Web of Science ®Google Scholar
• Çeken, S., Alkan, M., Smith, P. F. (2013). The dual notion of the prime radical of a module. J. Algebra 392:265–275. DOI: 10.1016/j.jalgebra.2013.06.015.
   Web of Science ®Google Scholar
• Fieldhouse, D.J. (1969). Pure theories. Math. Ann. 184(1):1–18. DOI: 10.1007/BF01350610.
   Web of Science ®Google Scholar
• Fuchs, L., Heinzer, W., Olberding, B. (2006). Commutative ideal theory without finiteness conditions: Irreducibility in the quotient filed. Abelian Groups, Rings, Modules, and Homological Algebra, Lect. Notes Pure Appl. Math. 249:121–145.
   Google Scholar
• Jayaram, C., Tekir, Ü. (2018). Von Neumann regular modules. Commun. Algebra 46(5):2205–2217. DOI: 10.1080/00927872.2017.1372460.
   Web of Science ®Google Scholar
• Ramamurthi, V.S., Rangaswamy, K.M. (1973). On finitely injective modules. J. Aust. Math. Soc. 16(2):239–248. DOI: 10.1017/S1446788700014294.
   Google Scholar
• Smith, P.F. (2015). Anti-homomorphisms between modules lattices. J. Commut. Algebra 7(4):567–592. DOI: 10.1216/JCA-2015-7-4-567.
   Web of Science ®Google Scholar
• von Neumann, J. (1936). On regular rings. Proc. Natl. Acad. Sci. USA. 22(12):707–713. DOI: 10.1073/pnas.22.12.707.
   PubMedGoogle Scholar
• Ware, R. (1971). Endomorphism rings of projective modules. Trans. Amer. Math. Soc. 155(1):233–256. DOI: 10.1090/S0002-9947-1971-0274511-2.
   Web of Science ®Google Scholar
• Wisbauer, R. (1991). Foundations of Modules and Rings Theory. Philadelphia: Gordon and Breach.
   Google Scholar
• Yassemi, S. (1995). Coassociated primes. Commun. Algebra 23(4):1473–1498. DOI: 10.1080/00927879508825288.
   Web of Science ®Google Scholar
• Yassemi, S. (2001). The dual notion of prime submodules. Arch. Math (Brno). 37:273–278.
   Google Scholar
• Zelmanowitz, J. (1972). Regular modules. Trans. Amer. Math. Soc. 163:341–355. DOI: 10.1090/S0002-9947-1972-0286843-3.
   Web of Science ®Google Scholar