اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe group invertibility of matrices over Bezout domains
155
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Let $R$ be a Bezout domain, and let $A,B,Cin R^{ntimes n}$ with $ABA=ACA$. If $AB$ and $CA$ are group invertible, we prove that $AB$ is similar to $CA$. Moreover, we have $(AB)^{#}$ is similar to $(CA)^{#}$. This generalize the main result of Cao and Li(Group inverses for matrices over a Bezout domain, {it Electronic J. Linear Algebra}, {bf 18}(2009), 600--612).
قيم البحث
اقرأ أيضاً
We study the theory of diagonal reductions of matrices over simple Ore domains of finite stable range. We cover the cases of 2-simple rings of stable range 1, Ore domains and certain cases of Bezout domains.
Let B be a commutative Bezout domain B and let MSpec(B) be the maximal spectrum of B. We obtain a Feferman-Vaught type theorem for the class of B-modules. We analyse the definable sets in terms, on one hand, of the definable sets in the classes of mo
dules over the localizations of B by the maximal ideals of B, and on the other hand, of the constructible subsets of MSpec(B). When B has good factorization, it allows us to derive decidability results for the class B-modules, in particular when B is the ring of algebraic integers or its intersection with real numbers or p-adic numbers.
We give some statements that are equivalent to the existence of group inverses of Peirce corner matrices of a $2 times 2$ block matrix and its generalized Schur complements. As applications, several new results for the Drazin inverses of the generali
zed Schur complements and the $2 times 2$ block matrix are obtained and some of them generalize several results in the literature.
Let $R$ be a commutative additively idempotent semiring. In this paper, some properties and characterizations for permanents of matrices over $R$ are established, and several inequalities for permanents are given. Also, the adjiont matrices of matrie
cs over $R$ are considered. Partial results obtained in this paper generalize the corresponding ones on fuzzy matrices, on lattice matrices and on incline matrices.
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
