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Inclines are additively idempotent semirings, in which the partial order ≤ : x ≤ y if and only if x + y = y is defined and products are less than or equal to either factor. Boolean algebra, max-min fuzzy algebra, and distributive lattices are examples of inclines. In this article, standard bases of a finitely generated vector space over a linearly ordered commutative incline are studied. We obtain that if a standard basis exists, then it is unique. In particular, if the incline is solvable or multiplicatively-declined or multiplicatively-idempotent (i.e., a chain semiring), further results are obtained, respectively. For a chain semiring a checkable condition for distinguishing if a basis is standard is given. Based on the condition an algorithm for computing the standard basis is described. 相似文献
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Igor Dolinka 《Semigroup Forum》2009,78(2):368-373
We generalize a criterion from a previous paper which ensures that an additively idempotent semiring is not finitely based.
As a consequence, we prove the NFB property for the semiring generated by transformations on a finite set with more than one
element.
Supported by Grant No. 144011 of the Ministry of Science of the Republic of Serbia. 相似文献
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引出半环中模糊点生成的模糊理想的定义,讨论了它的一些性质,并用它刻画了半环中素、半素、完全素、完全半素模糊理想,最后讨论了这几类理想的关系。 相似文献
5.
Seok-Zun Song Kyung-Tae Kang LeRoy B. Beasley Nung-Sing Sze 《Linear algebra and its applications》2008,429(1):209-223
An m×n matrix A over a semiring is called regular if there is an n×m matrix G over such that AGA=A. We study the problem of characterizing those linear operators T on the matrices over a semiring such that T(X) is regular if and only if X is. Complete characterizations are obtained for many semirings including the Boolean algebra, the nonnegative reals, the nonnegative integers and the fuzzy scalars. 相似文献
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In this paper, we consider matrices with entries from a semiring S. We first discuss some generalized inverses of rectangular and square matrices. We establish necessary and sufficient conditions for the existence of the Moore–Penrose inverse of a regular matrix. For an m×n matrix A , an n×m matrix P and a square matrix Q of order m, we present necessary and sufficient conditions for the existence of the group inverse of QAP with the additional property that P(QAP)#Q is a {1,2} inverse of A . The matrix product used here is the usual matrix multiplication. The result provides a method for generating elements in the set of {1,2} inverses of an m×n matrix A starting from an initial {1} inverse of A . We also establish a criterion for the existence of the group inverse of a regular square matrix. We then consider a semiring structure (Mm×n(S),+,°) made up of m×n matrices with the addition defined entry-wise and the multiplication defined as in the case of the Hadamard product of complex matrices. In the semiring (Mm×n(S),+,°), we present criteria for the existence of the Drazin inverse and the Moore–Penrose inverse of an m×n matrix. When S is commutative, we show that the Hadamard product preserves the Hermitian property, and provide a Schur-type product theorem for the product A°(CC?) of a positive semidefinite n×n matrix A and an n×n matrix C. 相似文献
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Shan ZhaoXue-ping Wang 《Fuzzy Sets and Systems》2011,182(1):93-100
This paper investigates the cardinality of a basis in semilinear spaces of n-dimensional vectors over join-semirings. First, it introduces the notion of an irredundant decomposition of an element in a join-semiring, then discusses the cardinality of a basis and proves that the cardinality of each basis is n if and only if the multiplicative identity element 1 is join-irreducible. If 1 is not a join-irreducible element then each basis need not have the same number of elements in semilinear spaces of n-dimensional vectors over join-semirings. This gives an answer to an open problem raised by Di Nola et al. in their work [Algebraic analysis of fuzzy systems, Fuzzy Sets and Systems 158 (2007) 1-22]. 相似文献
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We prove that the endomorphism semiring of a nontrivial semilattice is always subdirectly irreducible and describe its monolith.
The endomorphism semiring is congruence simple if and only if the semilattice has both a least and a largest element.
The third author was partially supported by the Hungarian National Foundation for Scientific Research (OTKA), grant nos. T 48809
and K 60148. The work is a part of the research project MSM0021620839 financed by MSMT. 相似文献
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Chebyshev type inequalities for pseudo-integrals 总被引:1,自引:0,他引:1
Hamzeh Agahi Radko Mesiar Yao Ouyang 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(6):2737-2743
Chebyshev type inequalities for two classes of pseudo-integrals are shown. One of them concerning the pseudo-integrals based on a function reduces on the g-integral where pseudo-operations are defined by a monotone and continuous function g. Another one concerns the pseudo-integrals based on a semiring ([a,b],max,⊙), where ⊙ is generated. Moreover, a strengthened version of Chebyshev’s inequality for pseudo-integrals is proved. 相似文献