Direct Decompositions of Matrices

2020 ◽  
pp. 77-87
Author(s):  
Adolf Mader ◽  
Otto Mutzbauer
Keyword(s):  
Direct Decompositions

scholarly journals Isometries and direct decompositions of pseudo MV-algebras

2007 ◽  
Vol 57 (2) ◽  
Author(s):  
Milan Jasem
Keyword(s):  
Direct Decomposition ◽  
The Other ◽  
Other Hand ◽  
Mv Algebra ◽  
Direct Decompositions ◽  
Mv Algebras

AbstractIn the paper isometries in pseudo MV-algebras are investigated. It is shown that for every isometry f in a pseudo MV-algebra $$\mathcal{A}$$ = (A, ⊕, −, ∼, 0, 1) there exists an internal direct decomposition $$\mathcal{A} = \mathcal{B}^0 \times \mathcal{C}^0 $$ of $$\mathcal{A}$$ with $$\mathcal{C}^0 $$ commutative such that $$f(0) = 1_{C^0 } $$ and $$f(x) = x_{B^0 } \oplus (1_{C^0 } \odot (x_{C^0 } )^ - ) = x_{B^0 } \oplus (1_{C^0 } - x_{C^0 } )$$ for each x ∈ A.On the other hand, if $$\mathcal{A} = \mathcal{P}^0 \times \mathcal{Q}^0 $$ is an internal direct decomposition of a pseudo MV-algebra $$\mathcal{A}$$ = (A, ⊕, −, ∼, 0, 1) with $$\mathcal{Q}^0 $$ commutative, then the mapping g: A → A defined by $$g(x) = x_{P^0 } \oplus (1_{Q^0 } - x_{Q^0 } )$$ is an isometry in $$\mathcal{A}$$ and $$g(0) = 1_{Q^0 } $$ .

scholarly journals Free Lie algebras as modules for symmetric groups

1999 ◽  
Vol 67 (2) ◽  
pp. 143-156 ◽  
Author(s):  
R. M. Bryant ◽  
L. G. Kovács ◽  
Ralph Stöhr
Keyword(s):  
Lie Algebras ◽  
Symmetric Groups ◽  
Free Lie Algebra ◽  
Prime Characteristic ◽  
Specht Modules ◽  
Generating Set ◽  
Direct Sum ◽  
Finite Dimensional ◽  
Free Lie Algebras ◽  
Direct Decompositions

AbstractLet r be a positive integer, F a field of odd prime characteristic p, and L the free Lie algebra of rank r over F. Consider L a module for the symmetric group , of all permutations of a free generating set of L. The homogeneous components Ln of L are finite dimensional submodules, and L is their direct sum. For p ≤ r ≤ 2p, the main results of this paper identify the non-porojective indecomposable direct summands of the Ln as Specht modules or dual Specht modules corresponding to certain partitions. For the case r = p, the multiplicities of these indecomposables in the direct decompositions of the Ln are also determined, as are the multiplicities of the projective indecomposables. (Corresponding results for p = 2 have been obtained elsewhere.)

scholarly journals The Jordan–Zassenhaus Theorem and Direct Decompositions

2000 ◽  
Vol 230 (2) ◽  
pp. 730-748 ◽  
Author(s):  
L. Fuchs ◽  
P. Vámos
Keyword(s):  
Direct Decompositions

Isomorphisms of direct decompositions in structures

1968 ◽  
Vol 9 (6) ◽  
pp. 1021-1038
Author(s):  
E. N. Mochul'skii
Keyword(s):  
Direct Decompositions
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