اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAlgebraic Semigroups are Strongly {pi}-regular
217
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Let $S$ be an algebraic semigroup (not necessarily linear) defined over a field $F$. We show that there exists a positive integer $n$ such that $x^n$ belongs to a subgroup of $S(F)$ for any $x in S(F)$. In particular, the semigroup $S(F)$ is strongly {pi}-regular.
قيم البحث
اقرأ أيضاً
We prove that an analogue of Jordans theorem on finite subgroups of general linear groups holds for the groups of biregular automorphisms of algebraic surfaces. This gives a positive answer to a question of Vladimir L. Popov.
Let M be an irreducible normal algebraic monoid with unit group G. It is known that G admits a Rosenlicht decomposition, G=G_antG_aff, where G_ant is the maximal anti-affine subgroup of G, and G_aff the maximal normal connected affine subgroup of G.
In this paper we show that this decomposition extends to a decomposition M=G_antM_aff, where M_aff is the affine submonoid M_aff=bar{G_aff}. We then use this decomposition to calculate $mathcal{O}(M)$ in terms of $mathcal{O}(M_aff)$ and G_aff, G_antsubset G. In particular, we determine when M is an anti-affine monoid, that is when $mathcal{O}(M)=K$.
Let $pi_1(C)$ be the algebraic fundamental group of a smooth connected affine curve, defined over an algebraically closed field of characteristic $p>0$ of countable cardinality. Let $N$ be a normal (resp. characteristic) subgroup of $pi_1(C)$. Under
the hypothesis that the quotient $pi_1(C)/N$ admits an infinitely generated Sylow $p$-subgroup, we prove that $N$ is indeed isomorphic to a normal (resp. characteristic) subgroup of a free profinite group of countable cardinality. As a consequence, every proper open subgroup of $N$ is a free profinite group of countable cardinality.
Recently Brosnan and Chow have proven a conjecture of Shareshian and Wachs describing a representation of the symmetric group on the cohomology of regular semisimple Hessenberg varieties for $GL_n(mathbb{C})$. A key component of their argument is tha
t the Betti numbers of regular Hessenberg varieties for $GL_n(mathbb{C})$ are palindromic. In this paper, we extend this result to all reductive algebraic groups, proving that the Betti numbers of regular Hessenberg varieties are palindromic.
We consider the lattice of subsemigroups of the general linear group over an Artinian ring containing the group of diagonal matrices and show that every such semigroup is actually a group.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
