Symmetry on zero and idempotents

References

• Alghazzawi, D., Leroy, A. G. (2019). Commutatively closed sets in rings. Commun. Algebra. 47(4):1629–1641. DOI: 10.1080/00927872.2018.1513011.
   Web of Science ®Google Scholar
• Amitsur, S. A. (1956). Radicals of polynomial rings. Canad. J. Math. 8:355–361. DOI: 10.4153/CJM-1956-040-9.
   Google Scholar
• Anderson, D. D., Camillo, V. (1999). Semigroups and rings whose zero products commute. Commun. Algebra. 27(6):2847–2852. DOI: 10.1080/00927879908826596.
   Web of Science ®Google Scholar
• Antoine, R. (2008). Nilpotent elements and Armendariz rings. J. Algebra. 319(8):3128–3140. DOI: 10.1016/j.jalgebra.2008.01.019.
   Web of Science ®Google Scholar
• Badawi, A. (1997). On Abelian π-regular rings. Commun. Algebra. 25(4):1009–1021. DOI: 10.1080/00927879708825906.
   Web of Science ®Google Scholar
• Bell, H. E. (1970). Near-rings in which each element is a power of itself. Bull. Austral. Math. Soc. 2(3):363–368. DOI: 10.1017/S0004972700042052.
   Google Scholar
• Camillo, V., Hong, C. Y., Kim, N. K., Lee, Y., Nielsen, P. P. (2010). Nilpotent ideals in polynomial and power series rings. Proc. Amer. Math. Soc. 138(5):1607–1619. DOI: 10.1090/S0002-9939-10-10252-4.
   Web of Science ®Google Scholar
• Choi, K. J., Kwak, T. K., Lee, Y. (2019). Reversibility and symmetry over centers. J. Korean Math. Soc. 56(3):723–738.
   Web of Science ®Google Scholar
• Cohn, P. M. (1999). Reversible rings. Bull. Lond. Math. Soc. 31(6):641–648. DOI: 10.1112/S0024609399006116.
   Web of Science ®Google Scholar
• Goodearl, K. R. (1979). Von Neumann Regular Rings. London: Pitman.
   Google Scholar
• Grothendieck, A., Dieudonné, J. (1960). Eléments de Géometrie Algébrique I. Paris: I.H.E.S. Publications Math.
   Google Scholar
• Huh, C., Kim, H. K., Kim, N. K., Lee, Y. (2005). Basic examples and extensions of symmetric ring. J. Pure Appl. Algebra. 202(1–3):154–167. DOI: 10.1016/j.jpaa.2005.01.009.
   Web of Science ®Google Scholar
• Huh, C., Lee, Y. (1998). A note on π-regular rings. Kyungpook Math. J. 38(1):157–161.
   Google Scholar
• Huh, C., Lee, Y., Smoktunowicz, A. (2002). Armendariz rings and semicommutative rings. Commun. Algebra. 30(2):751–761. DOI: 10.1081/AGB-120013179.
   Web of Science ®Google Scholar
• Hwang, S. U., Jeon, Y. C., Lee, Y. (2006). Structure and topological conditions of NI rings. J. Algebra. 302(1):186–199. DOI: 10.1016/j.jalgebra.2006.02.032.
   Web of Science ®Google Scholar
• Jung, D. W., Kim, N. K., Lee, Y., Ryu, S. J. (2015). On properties related to reversible rings. Bull. Korean Math. Soc. 52(1):247–261. DOI: 10.4134/BKMS.2015.52.1.247.
   Web of Science ®Google Scholar
• Kim, N. K., Lee, Y. (2000). On right quasi-duo rings which are π-regular. Bull. Korean Math. Soc. 37(2):217–227.
   Google Scholar
• Kim, N. K., Lee, Y. (2000). Armendariz rings and reduced rings. J. Algebra. 223(2):477–488. DOI: 10.1006/jabr.1999.8017.
   Web of Science ®Google Scholar
• Kim, N. K., Lee, Y. (2003). Extensions of reversible rings. J. Pure Appl. Algebra. 185(1–3):207–223. DOI: 10.1016/S0022-4049(03)00109-9.
   Web of Science ®Google Scholar
• Koh, K. (1971). On functional representations of a ring without nilpotent elements. Canad. Math. Bull. 14(3):349–352. DOI: 10.4153/CMB-1971-063-7.
   Google Scholar
• Lam, T. Y. (1991). A First Course in Noncommutative Rings. New York: Springer-Verlag.
   Google Scholar
• Lambek, J. (1966). Lectures on Rings and Modules. Waltham: Blaisdell Publishing Company.
   Google Scholar
• Lambek, J. (1971). On the representation of modules by sheaves of factor modules. Canad. Math. Bull. 14(3):359–368. DOI: 10.4153/CMB-1971-065-1.
   Web of Science ®Google Scholar
• Lee, Y. (2015). On generalizations of commutativity. Commun. Algebra. 43(4):1687–1697. DOI: 10.1080/00927872.2013.876035.
   Web of Science ®Google Scholar
• Lee, Y. (2018). On structure of unit-IFP rings. J. Korean Math. Soc. 55(5):1257–1268.
   Web of Science ®Google Scholar
• Marks, G. (2001). On 2-primal Ore extensions. Commun. Algebra. 29(5):2113–2123. DOI: 10.1081/AGB-100002173.
   Web of Science ®Google Scholar
• McConnell, J. C., Robson, J. C. (1987). Noncommutative Noetherian Rings. Chichester: John Wiley & Sons Ltd.
   Google Scholar
• McCoy, N. H. (1939). Generalized regular rings. Bull. Amer. Math. Soc. 45(2):175–178. DOI: 10.1090/S0002-9904-1939-06933-4.
   Google Scholar
• Xue, W. (1992). Structure of minimal noncommutative duo rings and minimal strongly bounded non-duo rings. Commun. Algebra. 20(9):2777–2788. DOI: 10.1080/00927879208824488.
   Web of Science ®Google Scholar