ALGEBRAS WITH A NILPOTENT GENERATOR OVER ℤp2

Title & Authors
ALGEBRAS WITH A NILPOTENT GENERATOR OVER ℤp2
Woo, Sung-Sik;

Abstract
The purpose of this paper is to describe the structure of the rings $\small{\mathbb{Z}_{p^2}[X]/({\alpha}(X))}$ with $\small{{\alpha}(X)}$ a monic polynomial and $\small{\={X}^{\kappa}=0}$ for some nonnegative integer $\small{{\kappa}}$. Especially we will see that any ideal of such rings can be generated by at most two elements of the special form and we will find the 'minimal' set of generators of the ideals. We indicate how to identify the isomorphism types of the ideals as $\small{\mathbb{Z}_{p^2}-modules}$ by finding the isomorphism types of the ideals of some particular ring. Also we will find the annihilators of the ideals by finding the most 'economical' way of annihilating the generators of the ideal.
Keywords
cyclic code over $\small{\mathbb{Z}_4}$;
Language
English
Cited by
1.
CYCLIC CODES OF EVEN LENGTH OVER Z4,;

대한수학회지, 2007. vol.44. 3, pp.697-706
2.
THE GROUP OF UNITS OF SOME FINITE LOCAL RINGS I,;

대한수학회지, 2009. vol.46. 2, pp.295-311
3.
IDEALS OF Zpn[X]/(Xl-1),;

대한수학회논문집, 2011. vol.26. 3, pp.427-443
1.
IDEALS OF Zpn[X]/(Xl-1), Communications of the Korean Mathematical Society, 2011, 26, 3, 427
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