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研究元素个数不超过6的真伪BCK-代数的计数问题.首先,证明了在元素个数不超过3的偏序集上不存在真伪BCK-代数.其次,引入NP-型偏序集(不存在真伪BCK-代数的含重大元的偏序集)、偏序集的层、次余原子等概念,证明了在一个层数n≤3的NP-型偏序集上添加孤立余原子(或孤立次余原子或上邻元的个数n≥3的极小次余原子)后得到的偏序集也是NP-型偏序集,由此得到26种NP-型偏序集(元素个数n≤6).最后,借助Matlab软件编程计算得出所有非同构的元素个数不超过6的真伪BCK-代数,其中元素个数为4的真伪BCK-代数2个,元素个数为5的真伪BCK-代数34个,元素个数为6的真伪BCK-代数631个. 相似文献
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Algebra word problem solving approaches in a chemistry context: Equation worked examples versus text editing 总被引:1,自引:0,他引:1
Text editing directs students’ attention to the problem structure as they classify whether the texts of word problems contain sufficient, missing or irrelevant information for working out a solution. Equation worked examples emphasize the formation of a coherent problem structure to generate a solution. Its focus is on the construction of three equation steps each of which comprises essential units of relevant information. In an experiment, students were randomly assigned to either text editing or equation worked examples condition in a regular classroom setting to learn how to solve algebra word problems in a chemistry context. The equation worked examples group outperformed the text editing group for molarity problems, which were more difficult than dilution problems. Empirical evidence supports the theoretical rationale in using equation worked examples to facilitate students’ construction of a coherent problem structure so as to develop problem skills and expertise to solve molarity problems. 相似文献
256.
Christopher Phan 《代数通讯》2013,41(3):834-844
Let A be a connected-graded algebra with trivial module 𝕜, and let B be a graded Ore extension of A. We relate the structure of the Yoneda algebra E(A): = Ext A (𝕜, 𝕜) to E(B). Cassidy and Shelton have shown that when A satisfies their 𝒦2 property, B will also be 𝒦2. We prove the converse of this result. 相似文献
257.
Wai-Shun Cheung 《Linear and Multilinear Algebra》2013,61(3):299-310
We investigate Lie derivations on a class of algebras called triangular algebras. In particular, we give sufficient conditions such that every Lie derivation on such an algebra <artwork name="GLMA31004ei1"> is a sum of derivation on <artwork name="GLMA31004ei2"> and a mapping from <artwork name="GLMA31004ei3"> to its centre. 相似文献
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The column rank of an m by n matrix A over max algebra is the weak dimension of the column space of A. We compare the column rank with rank of matrices over max algebra. We also characterize the linear operators which preserve the column rank of matrices over max algebra. 相似文献
259.
Let A⊂C(X) and B⊂C(Y) be uniform algebras with Choquet boundaries δA and δB. A map T:A→B is called norm-linear if ‖λTf+μTg‖=‖λf+μg‖; norm-additive, if ‖Tf+Tg‖=‖f+g‖, and norm-additive in modulus, if ‖|Tf|+|Tg|‖=‖|f|+|g|‖ for each λ,μ∈C and all algebra elements f and g. We show that for any norm-linear surjection T:A→B there exists a homeomorphism ψ:δA→δB such that |(Tf)(y)|=|f(ψ(y))| for every f∈A and y∈δB. Sufficient conditions for norm-additive and norm-linear surjections, not assumed a priori to be linear, or continuous, to be unital isometric algebra isomorphisms are given. We prove that any unital norm-linear surjection T for which T(i)=i, or which preserves the peripheral spectra of C-peaking functions of A, is a unital isometric algebra isomorphism. In particular, we show that if a linear operator between two uniform algebras, which is surjective and norm-preserving, is unital, or preserves the peripheral spectra of C-peaking functions, then it is automatically multiplicative and, in fact, an algebra isomorphism. 相似文献
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