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41.
42.
We show that, if a groupoid graded ring has a grading satisfying a certain nondegeneracy property, then the commutant of the center of the principal component of the ring has the ideal intersection property, that is it intersects nontrivially every nonzero ideal of the ring. Furthermore, we show that for skew groupoid algebras with commutative principal component, the principal component is maximal commutative if and only if it has the ideal intersection property. 相似文献
43.
Richard Varro 《代数通讯》2013,41(7):2426-2448
We give the identities generating the spaces of degree 4 multilinear identities satisfied by the non commutative 0th-order Bernstein algebras and the non commutative mutation algebras. For it, we use a method reducing the search for multilinear identities to the resolution of linear systems. 相似文献
44.
Nathan Bloomfield 《代数通讯》2013,41(2):765-775
To each commutative ring R we can associate a zero divisor graph whose vertices are the zero divisors of R and such that two vertices are adjacent if their product is zero. Detecting isomorphisms among zero divisor graphs can be reduced to the problem of computing the classes of R under a suitable semigroup congruence. Presently, we introduce a strategy for computing this quotient for local rings using knowledge about a generating set for the maximal ideal. As an example, we then compute Γ(R) for several classes of rings; with the results in [4] these classes include all local rings of order p 4 and p 5 for prime p. 相似文献
45.
We show that every ‐relative difference set D in relative to can be represented by a polynomial , where is a permutation for each nonzero a. We call such an f a planar function on . The projective plane Π obtained from D in the way of M. J. Ganley and E. Spence (J Combin Theory Ser A, 19(2) (1975), 134–153) is coordinatized, and we obtain necessary and sufficient conditions of Π to be a presemifield plane. We also prove that a function f on with exactly two elements in its image set and is planar, if and only if, for any . 相似文献
46.
刻画了某类特殊可换无零因子反环上保持矩阵{1}一逆的可逆线性算子,并将此结果推广到此类无零因子反环的任意直积上.推广了某些文献的一些结果. 相似文献
47.
《Discrete Mathematics》2022,345(7):112898
The Hamming distance between two equal-length words u, v is the number of positions where u and v differ. The words u and v are said to be conjugates if there exist non-empty words such that and . The smallest value can take on is 0, when x and y commute. But, interestingly, the next smallest value can take on is 2 and not 1. In this paper, we consider conjugates and where . More specifically, we provide an efficient formula to count the number of length-n words over a k-letter alphabet that have a conjugate such that . We also provide efficient formulae for other quantities closely related to . Finally, we show that grows erratically: cubically for n prime, but exponentially for n even. 相似文献
48.
49.
We study those functions that can be written as a finite sum of periodic integer valued functions. On ℤ we give three different
characterizations of these functions. For this we prove that the existence of a real valued periodic decomposition of a ℤ
→ ℤ function implies the existence of an integer valued periodic decomposition with the same periods. This result depends
on the representation of the greatest common divisor of certain polynomials with integer coefficients as a linear combination
of the given polynomials where the coefficients also belong to ℤ[x]. We give an example of an ℤ → {0, 1} function that has a bounded real valued periodic decomposition but does not have a
bounded integer valued periodic decomposition with the same periods. It follows that the class of bounded ℤ → ℤ functions
has the decomposition property as opposed to the class of bounded ℝ → ℤ functions. If the periods are pairwise commensurable
or not prescribed, then we get more general results.
Supported by OTKA grants T 43623 and K 61908. 相似文献
50.
In this paper, the structure of Jordan higher derivable maps on triangular algebras by commutative zero products is given. As an application, the form of Jordan higher derivable maps of nest algebras by commutative zero products is obtained. 相似文献