Quasi-coefficient rings of a local ring

Coefficient Subrings of Certain Local Rings with Prime-power Characteristic

If R is a local ring whose radical J(R) is nilpotent and R/J(R) is a commutative field which is algebraic over GF(p), then R has at least one subring S such that S w*=,S,, where each S, is isomorphic to a Galois ring and S/J(S) is naturally isomorphic to R/J(R). Such subrings ofR are mutually isomorphic, but not necessarily conjugate in R.

A class of Artinian local rings of homogeneous type

‎Let $I$ be an ideal in a regular local ring $(R,n)$‎, ‎we will find‎ ‎bounds on the first and the last Betti numbers of‎ ‎$(A,m)=(R/I,n/I)$‎. ‎if $A$ is an Artinian ring of the embedding‎ ‎codimension $h$‎, ‎$I$ has the initial degree $t$ and $mu(m^t)=1$‎, ‎we call $A$ a {it $t-$extended stretched local ring}‎. ‎This class of‎ ‎local rings is a natural generalization of the class of stretched ...

ساختار کلاسهایی از حلقه های z- موضعی و c- موضعی the structure of some classes of z-local and c-local rings

فرض کنیمr یک حلقه تعویض پذیر ویکدار موضعی باشدو(j(r رایکال جیکوبسن r و(z(r مجموعه مقسوم علیه های صفر حلقه r باشد.گوییم r یک حلقه z- موضعی است هرگاه j(r)^2=. .همچنین برای یک حلقه تعویض پذیر r فرض کنیم c یک عنصر ناصفر از (z( r باشد با این خاصیت که cz( r)=0 گوییم حلقه موضعی r یک حلقه c - موضعی است هرگاه و{0 و z(r)^2={cو z(r)^3=0, نیز xz( r)=0 نتیجه دهد که x عضو {c,0 } است. در این پایان نامه ساخ...

Quasi-Primitive Rings and Density Theory

Quasi - Reduced Rings

Let R be an arbitrary ring with identity. In this paper, we introduce quasi-reduced rings as a generalization of reduced rings and investigate their properties. The ring R is called quasi-reduced if for any a, b ∈ R, ab = 0 implies (aR) ∩ (Rb) is contained in the center of R. We prove that some results of reduced rings can be extended to quasi-reduced rings for this general settings. 2010 Mathe...