Semigroups generated by nilpotent transformations
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In this paper, the subsemigroup of Px, the semigroup of all partial transformations of a set X into itself, which is generated by the nilpotents of px, is studied.About:
This article is published in Journal of Algebra.The article was published on 1987-10-15 and is currently open access. It has received 29 citations till now. The article focuses on the topics: Semigroup & Product (mathematics).read more
Citations
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Nilpotents in semigroups of partial one-to-one order-preserving mappings.
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On the nilpotent ranks of certain semigroups of transformations
TL;DR: In this paper, it was shown that if 1 < r < re 2 then the rank and the nilpotent rank of (A) are both equal to re + 2 for all re.
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On the semigroup nature of superconformal symmetry
TL;DR: In this paper, a semigroup of N = 1 superconformal transformations is introduced and analyzed, which can describe transitions from body to soul and form a proper ideal containing a set of nilpotent transformations.
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Semigroups of linear endomorphisms closed under conjugation
João Araújo,Fernando C. Silva +1 more
TL;DR: In this paper, it was shown that singular endomorphisms of a finite dimensional vector space can be obtained if and only if rank(b) ≥ rank(a) of a.
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On the Number of Nilpotents in the Partial Symmetric Semigroup
A. Laradji,Abdullahi Umar +1 more
TL;DR: In this paper, the authors obtained and discussed formulae for the total number of partial and nilpotent partial one-one transformations of a finite set, and showed that the number of transformations can be reduced to
References
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Book
The algebraic theory of semigroups
A. H. Clifford,G. B. Preston +1 more
TL;DR: A survey of the structure and representation theory of semi groups is given in this article, along with an extended treatment of the more important recent developments of Semi Group Structure and Representation.
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On products of idempotent matrices
TL;DR: In this article, it was shown that every transformation of a finite set which is not a permutation can be written as a product of idempotents, which is a result for matrices.
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Products of idempotent matrices
TL;DR: For every field F and every pair (n,k) of positive integers, an n×n matrix S over F is a product of k idempotent matrices over F iff rank(I − S)⩽k· nullity S.
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The semigroup of endomorphisms of a Boolean ring
TL;DR: In this article, it was shown that if R and T are isomorphic rings, then (R and T) and (T) are semigroups under composition, then they are not isomorphic.