اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe Taylor resolution over a skew polynomial ring
270
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Let $Bbbk$ be a field and let $I$ be a monomial ideal in the polynomial ring $Q=Bbbk[x_1,ldots,x_n]$. In her thesis, Taylor introduced a complex which provides a finite free resolution for $Q/I$ as a $Q$-module. Later, Gemeda constructed a differential graded structure on the Taylor resolution. More recently, Avramov showed that this differential graded algebra admits divided powers. We generalize each of these results to monomial ideals in a skew polynomial ring $R$. Under the hypothesis that the skew commuting parameters defining $R$ are roots of unity, we prove as an application that as $I$ varies among all ideals generated by a fixed number of monomials of degree at least two in $R$, there is only a finite number of possibilities for the Poincar{e} series of $Bbbk$ over $R/I$ and for the isomorphism classes of the homotopy Lie algebra of $R/I$ in cohomological degree larger or equal to two.
قيم البحث
اقرأ أيضاً
In this paper, we exhibit the creation of the maximal integral domain mid(R) generated by a nonzero commutative ring R.
In the well-known construction of the field of fractions of an integral domain, division by zero is excluded. We introduce fracpairs as pairs subject to laws consistent with the use of the pair as a fraction, but do not exclude denominators to be zer
o. We investigate fracpairs over a reduced commutative ring (a commutative ring that has no nonzero nilpotent elements) and provide these with natural definitions for addition, multiplication, and additive and multiplicative inverse. We find that modulo a simple congruence these fracpairs constitute a common meadow, which is a commutative monoid both for addition and multiplication, extended with a weak additive inverse, a multiplicative inverse except for zero, and an additional element a that is the image of the multiplicative inverse on zero and that propagates through all operations. Considering a as an error-value supports the intuition. The equivalence classes of fracpairs thus obtained are called common cancellation fractions (cc-fractions), and cc-fractions over the integers constitute a homomorphic pre-image of the common meadow Qa, the field Q of rational numbers expanded with an a-totalized inverse. Moreover, the initial common meadow is isomorphic to the initial algebra of cc-fractions over the integer numbers. Next, we define canonical term algebras for cc-fractions over the integers and some meadows that model the rational numbers expanded with a totalized inverse, and provide some negative results concerning their associated term rewriting properties. Then we consider reduced commutative rings in which the sum of two squares plus one cannot be a zero divisor: by extending the equivalence relation on fracpairs we obtain an initial algebra that is isomorphic to Qa. Finally, we express negative conjectures concerning alternative specifications for these (concrete) datatypes.
In this paper we calculate the Witt ring W(C) of a smooth geometrically connected projective curve C over a finite field of characteristic different from 2. We view W(C) as a subring of W(k(C)) where k(C) is the function field of C. We show that the
triviality of the Clifford algebra of a bilinear space over C gives the main relation. The calculation is then completed using classical results for bilinear spaces over fields.
We prove simplicity, and compute $delta$-derivations and symmetric associative forms of algebras in the title.
In this paper we deal with the problem of computing the sum of the $k$-th powers of all the elements of the matrix ring $mathbb{M}_d(R)$ with $d>1$ and $R$ a finite commutative ring. We completely solve the problem in the case $R=mathbb{Z}/nmathbb{Z}
$ and give some results that compute the value of this sum if $R$ is an arbitrary finite commutative ring $R$ for many values of $k$ and $d$. Finally, based on computational evidence and using some technical results proved in the paper we conjecture that the sum of the $k$-th powers of all the elements of the matrix ring $mathbb{M}_d(R)$ is always $0$ unless $d=2$, $textrm{card}(R) equiv 2 pmod 4$, $1<kequiv -1,0,1 pmod 6$ and the only element $ein R setminus {0}$ such that $2e =0$ is idempotent, in which case the sum is $textrm{diag}(e,e)$.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
