J4 ›› 2010, Vol. 45 ›› Issue (8): 47-52.

• Articles • Previous Articles     Next Articles

Quasi-McCoy rings relative to a monoid

YANG Shi-zhou1, SONG Xue-mei2   

  1. 1. College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, Gansu, China;
    2. School of Mathematics, Lanzhou City University, Lanzhou 730070, Gansu, China
  • Received:2009-12-22 Online:2010-08-16 Published:2010-09-16


M-quasi-McCoy rings are introduced, and their properties are investigated. It is shown that, for any unique product monoid M, every reversible ring is M-quasi-McCoy. If M is a commutative and cancellative monoid containing an infinite cyclic submonoid, N is a u.p. monoid and R is a commutative M-quasiMcCoy ring, then R[N] is M-quasi-McCoy and R is M×N-quasi-McCoy. For a monoid M, R is M-quasi-McCoy ring if and only if upper triangular matrix ring Tn(R)  is M-quasi-McCoy ring and direct product ∏i∈IRi is M-quasi-McCoy ring if and only if each ring Ri(i∈I)  is M-quasi-McCoy ring.

Key words: monoid; unique product monoid; M-quasi-McCoy ring; M-quasi-Armendariz ring; upper triangular matrix ring; direct product

No related articles found!
Full text



No Suggested Reading articles found!