70.35 A Commutativity Theorem for Any Associative Operation

1986 ◽  
Vol 70 (453) ◽  
pp. 223
Author(s):  
Desmond Machale ◽  
Micheal O. Searcoid
Keyword(s):  
Commutativity Theorem ◽  
Associative Operation

scholarly journals A commutativity theorem for lefts-unital rings

1990 ◽  
Vol 13 (4) ◽  
pp. 769-774
Author(s):  
Hamza A. S. Abujabal
Keyword(s):  
Commutativity Theorem ◽  
Unital Ring ◽  
Commutativity Theorems ◽  
Associative Rings ◽  
Unital Rings

In this paper we generalize some well-known commutativity theorems for associative rings as follows: LetRbe a lefts-unital ring. If there exist nonnegative integersm>1,k≥0, andn≥0such that for anyx,yinR,[xky−xnym,x]=0, thenRis commutative.

On Irreduceability of Boolean Functions with Respect to Commutative Associative Operation

2020 ◽  
Vol 75 (4) ◽  
pp. 169-171
Author(s):  
G. V. Safonov ◽  
G. V. Bokov ◽  
V. B. Kudryavtsev
Keyword(s):  
Boolean Functions ◽  
Associative Operation

scholarly journals A Commutativity theorem for semiprime rings

1980 ◽  
Vol 30 (1) ◽  
pp. 33-36
Author(s):  
Vishnu Gupta
Keyword(s):  
Positive Integer ◽  
Semiprime Ring ◽  
Commutativity Theorem ◽  
Semiprime Rings

AbstractIt is shown that if R is a semiprime ring with 1 satisfying the property that, for each x, y ∈ R, there exists a positive integer n depending on x and y such that (xy)k − xkyk is central for k = n,n+1, n+2, then R is commutative, thus generalizing a result of Kaya.

scholarly journals Dispersal in compact semimodules

1972 ◽  
Vol 13 (3) ◽  
pp. 338-342 ◽  
Author(s):  
Alexander Doniphan Wallace
Keyword(s):  
Hausdorff Space ◽  
Continuous Operation ◽  
The Other ◽  
Associative Operation ◽  
Cox 1

A semigroup is a nonvoid Hausdorff space together with a continuous associative operation. A semiring is a nonvoid Hausdorff space together with a couple of continuous associative operations, one of which (usually denoted as multiplication) distributes over the other (usually denoted as addition). If R is a semiring then an R-semimodule is a semigroup M under addition together with a continuous operation R × M → M which satisfies the associativity and distributivity conditions usually stipulated in the instance of an R-module. It is purpose of this paper to establish for semimodules certain propositions proved by Kaplansky [4], Pearson [8], Selden [9], Beidleman-Cox [1] and others.

scholarly journals A generalized commutativity theorem for pk-quasihyponormal operators

Filomat ◽  
2007 ◽  
Vol 21 (2) ◽  
pp. 77-83
Author(s):  
B.P. Duggal
Keyword(s):  
Hilbert Space ◽  
Generalized Derivation ◽  
Elementary Operator ◽  
Commutativity Theorem ◽  
Hilbert Space Operators

For Hilbert space operators A and B, let ?AB denote the generalized derivation ?AB(X) = AX - XB and let /\AB denote the elementary operator rAB(X) = AXB-X. If A is a pk-quasihyponormal operator, A ? pk - QH, and B*is an either p-hyponormal or injective dominant or injective pk - QH operator (resp., B*is an either p-hyponormal or dominant or pk - QH operator), then ?AB(X) = 0 =? SA*B*(X) = 0 (resp., rAB(X) = 0 =? rA*B*(X) = 0). .

A Commutativity Theorem for Rings with Involution

1978 ◽  
Vol 30 (6) ◽  
pp. 1121-1143
Author(s):  
M. Chacron
Keyword(s):  
Prime Ring ◽  
Associative Ring ◽  
Commutativity Theorem ◽  
Period 2 ◽  
Rings With Involution ◽  
Symmetric Element

A ring with involution R is an associative ring endowed with an antiautomorphism * of period 2. One of the first commutativity results for rings with * is a theorem of S. Montgomery asserting that if R is a prime ring, in which every symmetric element s = s* is of the form s — sn(s) (n(s) ≧ 2), then either R is commutative or R is the 2 X 2 matrices over a field, which is a nice generalization of a well-known theorem of N. Jacobson on rings all of whose elements x = xn(x).

scholarly journals Embedding a semigroup of transformations

1975 ◽  
Vol 20 (2) ◽  
pp. 222-224
Author(s):  
J. S. V. Symons
Keyword(s):  
Associative Operation ◽  
Image Position ◽  
Semigroup Of Transformations

Let X be an arbitrary set and θ a transformation of X. One may use θ to induce an associative operation in Jx, the set of all mappings of X to itself as follows: . We denote the resulting semigroup by {Jx;θ) Magill (1967) introduced this structure and it has been studied by Sullivan and by myself.

Sign in / Sign up

Export Citation Format

Share Document