By J. L. S. Chen, N. Q. Ding
The chosen papers during this quantity hide all of the most vital parts of ring idea and module thought equivalent to classical ring idea, illustration concept, the idea of quantum teams, the speculation of Hopf algebras, the idea of Lie algebras and Abelian team conception. The assessment articles, written through experts, offer a very good evaluation of a few of the parts of ring and module thought - perfect for researchers trying to find a brand new or similar box of analysis. additionally integrated are unique articles exhibiting the craze of present examine.
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Extra resources for Advances in Ring Theory
Near-rings, Proc. Edinburgh Math. Soc. 26 (1983), 361-370. 8. J. D. P. Meldrum, Near-rings and Their Links with Groups, Pitman, Boston, London, Melbourne, 1985. 9. G. Pilz, Near-rings, North Holland, Amsterdam, New York, 1983. 10. R. P. Sullivan, Research problem No. 23, Period. Math. Hungar. 8 (1977), 313-314. nz We present a brief survey of the local semi-T-nilpotency condition on families of modules, with some indication of its uses and connections with other module properties. 1. The definition and introduction The local semi-T-nilpotency condition evolved in the 1970's in a series of papers, including , , , , , by M.
Lyons and J. D. P. G. near-rings, Proc. Amer. Math. Soc. 72 (1978), 221-227. 4. C. J. Maxson and K. C. Smith, The centralizer of a group endomorphism, J. Algebra 57 (1979), 441-448. 5. C. J. Maxson and K. C. Smith, Simple near-ring centralizers of finite rings, Proc. Amer. Math. Soc. 75 (1979), 8-12. 6. C. J. Maxson and A. B. Van der Merwe, Forcing linearity numbers for modules over rings with nontrivial idempotents, J. Algebra 256 (2002), 66-84. 7. J. D. P. G. near-rings, Proc. Edinburgh Math.
3). By (1), R is left and right morphic. Hence Zr(R) = Zt(R) = J(R) by [2, Theorem 24], so R is left and right nonsingular by (2). (4). R is not regular because its image C is not regular. 1. By Erlich , every unit regular ring is morphic, and every regular left morphic ring is unit regular. 393] raised the question whether a morphic ring R with J(R) = 0 is necessarily regular. This is shown to be false in general by Example 3. 232], it was asked whether a semiprime ring R such that every principal one-sided ideal is the annihilator of an element of R is regular or whether a left nonsingular ring R such that every principal one-sided ideal is the annihilator of an element of R is regular.