Results 81 to 90 of about 1,137 (186)
Linear and Multilinear AlgebraLet $T$ be an operator on Banach space $X$ that is similar to $- T$ via an involution $U$. Then $U$ decomposes the Banach space $X$ as $X = X_1 \oplus X_2$ with respect to which decomposition we have $U = \left(\begin{matrix} I_1 & 0 \\ 0 & -I_2 \end{matrix} \right)$, where $I_i$ is the identity operator on the closed subspace $X_i$ ($i=1, 2$).
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Translatability and translatable semigroups
Open Mathematics, 2018 The concept of a k-translatable groupoid is explored in depth. Some properties of idempotent k-translatable groupoids, left cancellative k-translatable groupoids and left unitary k-translatablegroupoids are proved. Necessary and sufficient conditions are
Dudek Wieslaw A., Monzo Robert A. R.
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Journal of Algebra, 1999 The Milnor-Moore theorem says that in characteristic zero, any connected graded cocommutative bialgebra \(A\) is canonically isomorphic to the enveloping bialgebra of the Lie algebra of its primitive elements \(\text{Prim}(A)\). There is a weaker form known as the Leray theorem, whose dual statement is that any retract of the vector space inclusion of \
Patras, Frédéric +1 more
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Skew Continuous Morphisms of Ordered Lattice Ringoids
Mathematics, 2016 Skew continuous morphisms of ordered lattice semirings and ringoids are studied. Different associative semirings and non-associative ringoids are considered. Theorems about properties of skew morphisms are proved. Examples are given.
Sergey Victor Ludkowski
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Special MatricesA nonzero element aa is called 1-Sylvester in a ring RR, if there exist b,c∈Rb,c\in R such that 1=ab+ca1=ab+ca. In this article, we study such elements, mainly in matrix rings over commutative rings.
Călugăreanu Grigore
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On Constructing Orthogonal Idempotents
Rocky Mountain Journal of Mathematics, 2007 Let \(A\) be a commutative semisimple algebra over an algebraically closed field. Let \(e_1,\dots,e_{n-1}\), where \(3\leq n\leq\dim A\), be nontrivial orthogonal idempotents in \(A\) such that \(e_1,\dots,e_{n-2}\) are minimal. It is shown that then there exist nontrivial orthogonal idempotents \(q_1,\dots,q_n\) with \(q_1,\dots,q_{n-1}\) minimal.
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Residuated Structures Derived from Commutative Idempotent Semirings
Discussiones Mathematicae - General Algebra and Applications, 2019 Since the reduct of every residuated lattice is a semiring, we can ask under what condition a semiring can be converted into a residuated lattice. It turns out that this is possible if the semiring in question is commutative, idempotent, G-simple and ...
Chajda Ivan, Länger Helmut
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A method for constructing idempotents in a unital algebra
Учёные записки Казанского университета: Серия Физико-математические наукиA method is proposed for constructing idempotents in a unital algebra 𝒜 using n arbitrary idempotents P1,...,Pn from this algebra. The properties of the resulting idempotents P = P(P1,...,Pn) are investigated; for n = 2 and n = 3, explicit forms of the ...
M. Khadour
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Idempotents for derangement numbers
Discrete Mathematics, 2003 The principal result of this paper locates a set of orthogonal idempotents in Solomon's descent algebra. The representations of the symmetric group arising from these idempotents have dimensions which are equal to the number of permutations with a particular number of fixed points.
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Publications mathématiques de Besançon. Algèbre et théorie des nombresPrevious work established the set of square-free integers n with at least one factorization n = p
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