# One-sided Duo rings are McCoy

@article{Cary2015OnesidedDR, title={One-sided Duo rings are McCoy}, author={Michael Cary}, journal={arXiv: Rings and Algebras}, year={2015} }

In this paper we prove that one-sided Duo rings are (two-sided) McCoy. By doing so, we are then able to explicitly describe some of these ring element annihilators of polynomials in McCoy rings. We conclude the paper by showing the place of these results in the literature by way of an extension of a convenient diagram from a paper by Camillo and Nielsen.

## References

SHOWING 1-10 OF 15 REFERENCES

### ANNIHILATORS IN IDEALS OF COEFFICIENTS OF ZERO-DIVIDING POLYNOMIALS

- Mathematics
- 2014

We continue the study of the McCoy ring property through examining constant annihilators in the ideals of coefficients of zero-dividing polynomials. In the process we introduce the ideal-McCoy…

### The McCoy Condition on Noncommutative Rings

- Mathematics
- 2011

McCoy proved in 1957 [12] that if a polynomial annihilates an ideal of polynomials over any ring then the ideal has a nonzero annihilator in the base ring. We first elaborate this McCoy's famous…

### Duo, Bézout, and Distributive Rings of Skew Power Series

- Mathematics
- 2009

We give necessary and sufficient conditions on a ring R and an endomorphism σ of R for the skew power series ring R[[x; σ]] to be right duo right Bezout. In particular, we prove that R[[x; σ]] is…

### Annihilators in Polynomial Rings

- Mathematics
- 1957

It is known that if f is a divisor of zero in the polynomial ring R [x], where R is a commutative ring, there exists a non-zero element c of R such that cf=0. Proofs of this theorem have been given…

### ON A RING PROPERTY UNIFYING REVERSIBLE AND RIGHT DUO RINGS

- Mathematics
- 2013

The concepts of reversible, right duo, and Armendariz rings are known to play important roles in ring theory and they are indepen- dent of one another. In this note we focus on a concept that can…

### Prime ideals and sheaf representation of a pseudo symmetric ring

- Mathematics
- 1973

Almost symmetric rings and pseudo symmetric rings are introduced. The classes of symmetric rings, of almost symmetric rings, and of pseudo symmetric rings are in a strictly increasing order. A sheaf…