SEMIRADICAL EQUALITY

SEMIRADICAL EQUALITY

Semiprime radical of a module is defined and the relation betweenthe intersection of prime submodules and the intersection of semiprime submodules is investigated. Semiradical formula is defined and it is shown thatcartesian product of M× M2satisfies the semiradical formula if and only ifM1and Msatisfy the semiradical formula

___

  • J. Jenkins and P. F. Smith, On the prime radical of a module over a commutative ring, Comm. in Algebra. Vol:20, No.12 (1992), 3593 – 3602.
  • A. Azizi and A. Nikseresht, On radical formula in modules, Glasgow. Math. J. Vol:53, No.3 (2011), 657 – 668.
  • A. Parkash, Arithmetical rings satisfy the radical formula, Journal of Commutative Algebra. Vol:4, No.2 (2012), 293 – 296.
  • E. Ylmaz and S. Klarslan Cansu, Baer’s lower nilradical and classical prime submodules, Bul. Iran Math. Soc., to appear.
  • M. Alkan and Y. Tra, On prime submodules, Rocky Mountain Journal of Mathematics, Vol:37, No.3 (2007), 709 – 722.
  • S. Atani and F. K. Saraei, Modules which satisfy the radical formula, Int. J. Contemp. Math. Sci. Vol:2, No.1 (2007), 13 – 18.
  • Abant Izzet Baysal University, Science and Art Faculty, Department of Mathemat
  • ics, Bolu-TURKEY E-mail address: kilicarslan s@ibu.edu.tr