Topic
Idempotence
About: Idempotence is a research topic. Over the lifetime, 1860 publications have been published within this topic receiving 19976 citations. The topic is also known as: idempotent.
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TL;DR: It is shown that Greibach’s normal form theorem depends only on a few equational properties of least pre-fixed points in semirings, and eliminations of chain and deletion rules depend on their inequational properties (and the idempotence of addition).
24 citations
TL;DR: In this paper, it was shown that if a cell (i,i) is occupied by a symbol, for each i, 1 < i < n, then the partial latin square is idempotent.
Abstract: A partial latin square on t symbols
24 citations
TL;DR: In this article, it was shown that a regular semigroup is always a regular subsemigroup of S and investigated relationships between it and S, where = S is of particular interest.
Abstract: Suppose S is a regular semigroup and E is its set of idempotents. If E is subsemigroup of S, then S has been called orthodox and studied recently by Hall [3], Meakin [6], and Yamada [8]. In this paper we assume that E is not (necessarily) a subsemigroup of S and consider the subsemigroup generated by E, denoted . If E denotes the set of all elements of S which can be written E, denoted . If E denotes the set of all elements of S which can be written as the product of n (not necessarily distinct) idempotents of S, then . We show that is always a regular subsemigroup of S and investigate relationships between it and S. The case where = S is of particular interest to us; such semigroups will be referred to as idempotent-generated regular semi- groups.
24 citations
TL;DR: In this article, a stability theorem for the nullity of a linear combination c1P1 + c2P2 of two idempotent operators P1, P2 on a Banach space provided c 1, c 2 and c 1 + c 2 are nonzero is proved.
Abstract: We prove a stability theorem for the nullity of a linear combination c1P1 + c2P2 of two idempotent operators P1, P2 on a Banach space provided c1, c2 and c1 + c2 are nonzero. We then show that for c1P1 + c2P2 the property of being upper semi-Fredholm, lower semi-Fredholm and Fredholm, respectively, is independent of the choice of c1, c2, and that the nullity, defect and index of c1P1 + c2P2 are stable.
24 citations
TL;DR: In this paper, the authors extend the central idempotent measure theorem to products of certain groups, including unitary groups, and show that it is valid for connected simple Lie groups.
Abstract: Let G be a compact group with dual object r = r(C) and let M(G) be the convolution algebra of regular finite Borel measures on G. The author has characterized the central idempotent measures on certain G, including the unitary groups, in terms of the hypercoset structure of r. The charac. terization also says that, on certain G, a central idempotent measure is a sum of such measures each of which is absolutely continuous with respect to the Haar measure of a closed normal subgroup. Ihe main result of this paper is an extension of this characterization to products of certain groups. The known structure of connected groups and a recent result of Ragozin on connected simple Lie groups will then show that the characterization is valid for connected groups. On the other hand, a simple example will show it is false in general for nonconnected groups. This characterization was done by Cohen for abelian groups and the proof borrows extensively from Amemiya and Ito's simplified proof of Cohen's result. 1. Canonical measures. Throughout the paper G will be a compact group. The dual object r of G is the set of equivalence classes of irreducible unitary representations of G. For a e r, X a will denote the character of the class and d(a) its degree. For ease of notation we define 'la= XJ/d(a). A measure it E MZ(G), the center of M(G), has a Fourier-Stieltjes transform A(i(a) = J VadA (a e r). A is idempotent, that is J. *p =g,U provided '(a) is always 0 or 1. J(G) will denote the class of central idempotent measures on G. If H is a closed subgroup of G let )1H denote the normalized Haar measure of H. 9IH is idempotent; )RH e J(G) provided H is normal. It is convenient to consider a larger class F(G) = Eg e MZ(G): ,(a) is an integerl. Received by the editors March 12, 1973. AMS (MOS) subject classifications (1970). Primary 22CO5, 43A05; Secondary 43A40.
24 citations