arXiv 1606.024502016-06-12math.RA

Centralizer's applications to the inverse along an element

Huihui Zhu, Jianlong Chen, Pedro Patricio, Xavier Mary

备注：: 14 pages

英文摘要：

In this paper, we first prove that the absorption law for one-sided inverses along an element holds, deriving the absorption law for the inverse along an element. We then apply this result to obtain the absorption law for the inverse along different elements. Also, the reverse order law and the existence criterion for the inverse along an element are given by centralizers in a ring. Finally, we characterize the Moore-Penrose inverse by one-sided invertibilities in a ring with involution.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

归纳的中心化子和逆作为范畴等价

Centralizers and Inverses to Induction as Equivalence of Categories

给定环同态$B \to A$，考虑它的中心化子$R = A^B$，双模自同态环$S = \End {}_BA_B$和次张量平方环$T = (A ø_B A)^B$ .循环模$R_T$或${}_SR$的非结合张量导致了在$A \| B$是可分的、H-可分的、分裂的或左深度2（D2）的情况下，与限制$A$-模的归纳函子或$B$ -模的限制上归纳函子逆的范畴等价。如果$R_T$或${}_SR$是投射的，这个性质刻画了环扩张的可分性或分裂性。只有在H-可分性的情况下，$R_T$才是一个progenerator，它取代了Azumaya代数$A$的关键模块$A_{A^e}$。建立这些特征后，我们刻画左D2扩张的模块$T_R$，并询问是否弱生成条件$R_T$可能表征左D2扩张以及，可能是一个问题，在$σ(M)$范畴或其推广。我们还证明了深度为2的扩张的中心化子是正规的Rieffel意义下的子环，也是预辫交换的。例如，它的正规性产生一个Hopf子代数模拟的一个factoid的子群和他们的中心化，和一个特殊的情况下猜想，D2 Hopf子代数是正常的。

2005-06-02math.CTmath.RA

沿乘积的逆及其应用

The inverse along a product and its applications

在本文中，我们研究最近定义的逆沿元素的概念。给出了环中沿乘积的逆的存在性准则。作为应用，给出了逆存在的等价条件和逆的表达式。

2014-11-28math.RA

Reverse order law for the inverse along an element

In this paper, we introduce a new concept called left (right) g-MP inverse in a $*$-monoid. The relations of this type of generalized inverse with left inverse along an element are investigated. Also, the reverse order law for the inverse along an element is studied. Then, the existence criteria and formulae of the inverse of the product of triple elements along an element are investigated in a monoid. Finally, we further study left and right g-MP inverses, the inverse along an element in the context of rings.

2016-02-24math.RA

环中沿元素的逆

The inverse along an element in rings

本文将在幺环的背景下研究沿元素的逆的几个性质。新的特征的存在性，这逆将被证明。此外，将充分描述沿着固定元素的所有可逆元素的集合。因此，沿着一个元素的交换逆将被表征。还将考虑群逆、（广义）Drazin逆和Moore-Penrose逆（在具有对合的环中）的特殊情况。

2015-07-20math.RA

On one-sided (B,C)-inverses of arbitrary matrices

In this article one-sided (b, c)-inverses of arbitrary matrices as well as one-sided inverses along a (not necessarily square) matrix, will be studied. In adddition, the (b, c)-inverse and the inverse along an element will be also researched in the context of rectangular matrices.

2017-01-31math.RA

The generalized inverses of the quaternion tensor via the T-product

In this article, specific definitions of the Moore-Penrose inverse, Drazin inverse of the quaternion tensor and the inverse along two quaternion tensors are introduced under the T-product. Some characterizations, representations and properties of the defined inverses are investigated. Moreover, algorithms are established for computing the Moore-Penrose inverse, Drazin inverse of the quaternion tensor and the inverse along two quaternion tensors, respectively.

2022-11-05math.RA

更多相关论文收起更多论文

长度为2的局部环上矩阵的相似性

Similarity of matrices over local rings of length two

设$R$是一个长为2的局部主理想环，例如，环$R=\Z/p^2\Z$具有$p$素数.在本文中，我们发展了一个理论的相似类的矩阵环$M_n(R)$的正规形解释他们的$R[t]$ -模的扩张。利用这一理论，我们描述了相似性类的$M_n(R)$为$n\leq 4$，以及他们的中心。在这些类中，我们刻画了与它们的转置相似的类。所有$n>3$都存在非自转置类。当$R$具有$q$阶的有限剩余域时，我们在$q$中以多项式的形式列举了相似类及其中心化子的基数.令人惊讶的是，在$M_n(R)$中表示相似性类的数量的多项式原来具有非负整数系数。

2013-09-11math.GRmath.RA

One-sided $(b, c)$-inverses in rings

In this paper we introduce a new generalized inverse in a ring -- one-sided $(b, c)$-inverse, derived as an extension of $(b, c)$-inverse. This inverse also generalizes one-sided inverse along an element, which was recently introduced by H. H. Zhu et al. [H. H. Zhu, J. L. Chen, P. Patrício, Further results on the inverse along an element in semigroups and rings, Linear Multilinear Algebra, 64 (3) (2016) 393-403]. Also, here we present one-sided annihilator $(b, c)$-inverse, which is an extension of the annihilator $(b, c)$-inverse. Necessary and sufficient conditions for the existence of these…

2016-07-21math.RA

The reverse order law of the $(b, c)$-inverse in rings

We present equivalent conditions of reverse order law for the $(b, c)$-inverse $(aw)^{(b,c)}=w^{(b,s)}a^{(t,c)}$ to hold in a ring. Also, we study various mixed-type reverse order laws for the $(b,c)$-inverse. As a consequence, we get results related to the reverse order law for the inverse along an element. More general case of reverse order law $(a_1a_2)^{(b_3, c_3)}=a_2^{(b_2, c_2)}a_1^{(b_1, c_1)}$ is considered too.

2016-07-27math.RA

The (b, c)-inverse in semigroups and rings with involution

In this paper, we first prove that if a is both left (b, c)-invertible and left (c, b)-invertible, then a is both (b, c)-invertible and (c, b)-invertible in a *-monoid, which generalized the recent result about the inverse along an element by Wang and Mosic, under the conditions (ab)* = ab and (ac)* = ac. In addition, we consider that ba is (c, b)- invertible, and at the same time ca is (b, c)-invertible under the same conditions, which extend the related results about Moore-Penrose inverses by Chen et al. to (b, c)-inverses. As applications, we obtain that under condition (a2)* = a2, a is an …

2019-11-06math.RA

半群、环、Banach和算子代数中元素的自然广义逆与核

Natural generalized inverse and core of an element in semigroups, rings and Banach and Operator Algebras

利用最近的逆的概念沿一个元素在一个半群，和自然偏序的幂等元，我们研究双交换广义逆，并定义了一个新的逆称为自然逆，广义Drazin逆在一个半群，但也Koliha-Drazin逆在一个环。在这种情况下，我们得到一个类似于幂零分解，Kato或Mbekhta分解的核心分解。在Banach和算子代数中，我们指出了谱的研究是不充分的，并利用局部谱理论的思想来研究这种新的逆。

2012-03-16math.GRmath.OAmath.RA

群，Moore-Penrose，核与对合环的对偶核逆

Group, Moore-Penrose, core and dual core inverse in rings with involution

设$R$是一个具有对合的环.最近引入的核心和双核逆的概念，从矩阵推广到任意$*$ -环的情况。证明了群、Moore-Penrose、核和对偶核逆是密切相关的，它们可以用适当的幂等元以同样的方式处理。给出了这些逆的几个特征。得到了一些新的性质，推广了一些已知的结果。得到了$R$中EP元素的一些特征。证明了核和对偶核逆属于沿元素的逆类和$(b,c)$ -逆类。特别考虑了$R$是希尔伯特空间上所有有界线性算子的代数的情况。

2014-03-26math.RAmath.RT