Involutions and Anticommutativity in Group Rings
نویسندگان
چکیده
منابع مشابه
Reversible Rings with Involutions and Some Minimalities
In continuation of the recent developments on extended reversibilities on rings, we initiate here a study on reversible rings with involutions, or, in short, ∗-reversible rings. These rings are symmetric, reversible, reflexive, and semicommutative. In this note we will study some properties and examples of ∗-reversible rings. It is proved here that the polynomial rings of ∗-reversible rings may...
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If ∗ : G → G is an involution on the finite group G, then ∗ extends to an involution on the integral group ring Z[G]. In this paper, we consider whether bicyclic units u ∈ Z[G] exist with the property that the group 〈u, u∗〉, generated by u and u∗, is free on the two generators. If this occurs, we say that (u, u∗) is a free bicyclic pair. It turns out that the existence of u depends strongly upo...
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If ∗ : G → G is an involution on the finite group G, then ∗ extends to an involution on the integral group ring Z[G]. In this paper, we consider whether bicyclic units u ∈ Z[G] exist with the property that the group 〈u, u∗〉, generated by u and u∗, is free on the two generators. If this occurs, we say that (u, u∗) is a free bicyclic pair. It turns out that the existence of u depends strongly upo...
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Several important combinatorial arrays, after inserting some minus signs, turn out to be involutions when considered as lower triangular matrices. Among these are the Pascal, RNA, and directed animal matrices. These examples and many others are in the Bell subgroup of the Riordan group. We characterize all such pseudo-involutions by means of a single sequence called the ∆-sequence. Finally we c...
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ژورنال
عنوان ژورنال: Canadian Mathematical Bulletin
سال: 2013
ISSN: 0008-4395,1496-4287
DOI: 10.4153/cmb-2011-178-2