Semigroups of valuations on local rings

Orderings and Valuations on Twisted Polynomial Rings

The real spectra of certain \twisted" polynomial algebras A over R are examined. In certain cases, including Weyl algebras and universal enveloping algebras of solvable Lie algebras, the stability indices of the residue spaces of Sper(A) are estimated. The results show that the Brr ocker-Scheiderer theory of minimal generation of constructible sets applies to Sper(A) in these cases. An attempt ...

Approximation theorems for valuations on commutative rings

Semigroups , Rings , and Markov

We analyze random walks on a class of semigroups called \left-regular bands". These walks include the hyperplane chamber walks of Bidi-gare, Hanlon, and Rockmore. Using methods of ring theory, we show that the transition matrices are diagonalizable and we calculate the eigenvalues and multiplicities. The methods lead to explicit formulas for the projections onto the eigenspaces. As examples of ...

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...

DISCRETE VALUATIONS CENTERED ON LOCAL DOMAINSReinhold

We study applications of discrete valuations to ideals in analytically irreducible domains, in particular applications to zero divisors modulo powers of ideals. We prove a uniform version of Izumi's theorem and calculate several examples illustrating it, such as for rational singularities. The paper contains a new criterion of analytic irreducibility, a new criterion of one-beredness, and a val...