scholarly journals Further results of special elements in rings with involution

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3381-3393
Author(s):  
Dijana Mosic ◽  
Sanzhang Xu ◽  
Julio Benítez
Keyword(s):  
Partial Isometries ◽  
Rings With Involution ◽  
Invertible Elements

In this paper, we consider Moore-Penrose invertible, group invertible, and core invertible elements in rings with involution to characterize EP, generalized normal, generalized Hermitian elements and generalized partial isometries. As a consequence, we obtain new characterizations for elements in rings with involution to be normal and Hermitian elements.

scholarly journals Core partial order in rings with involution

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5695-5701 ◽  
Author(s):  
Xiaoxiang Zhang ◽  
Sanzhang Xu ◽  
Jianlong Chen
Keyword(s):  
Partial Order ◽  
Partial Orders ◽  
Reverse Order ◽  
Unital Ring ◽  
Reverse Order Law ◽  
Rings With Involution ◽  
Invertible Elements

Let R be a unital ring with involution. Several characterizations and properties of core partial order in R are given. In particular, we investigate the reverse order law (ab)# = b#a# for two core invertible elements a, b ? R. Some relationships between core partial order and other partial orders are obtained.

On some orders in ∗-rings based on the core-EP decomposition

2020 ◽  
pp. 2250010
Author(s):  
Janko Marovt ◽  
Dijana Mosić
Keyword(s):  
Partial Order ◽  
The Core ◽  
Unital Ring ◽  
Rings With Involution ◽  
Invertible Elements ◽  
Unital Rings ◽  
Minus Partial Order

We study certain relations in unital rings with involution that are derived from the core-EP decomposition. The notion of the WG pre-order and the C-E partial order is extended from [Formula: see text], the set of all [Formula: see text] matrices over [Formula: see text], to the set [Formula: see text] of all core-EP invertible elements in an arbitrary unital ring [Formula: see text] with involution. A new partial order is introduced on [Formula: see text] by combining the WG pre-order and the well known minus partial order, and a new characterization of the core-EP pre-order in unital proper ∗-rings is presented. Properties of these relations are investigated and some known results are thus generalized.

scholarly journals On the Covariance of Moore-Penrose Inverses in Rings with Involution

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Hesam Mahzoon
Keyword(s):  
Regular Element ◽  
Relative Topology ◽  
Rings With Involution ◽  
Invertible Elements

We consider the so-called covariance set of Moore-Penrose inverses in rings with an involution. We deduce some new results concerning covariance set. We will show that ifais a regular element in aC∗-algebra, then the covariance set ofais closed in the set of invertible elements (with relative topology) ofC∗-algebra and is a cone in theC∗-algebra.

On the Topologically Invertible Elements of a Topological Algebra

2007 ◽  
Vol 107 (1) ◽  
pp. 73-80
Author(s):  
Hugo Arizmendi-Peimbert ◽  
Angel Carrillo-Hoyo
Keyword(s):  
Topological Algebra ◽  
Invertible Elements
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