Semiperfect countable C -finite semigroups S satisfying S = S + S

Bisgaard, Torben Maack

doi:10.1007/s002080050320

Cited by 7 publications

(28 citation statements)

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“…Just as [7] was going to press, it turned out that a semiperfect countable R-separative C-finite semigroup S automatically satisfies S = S + S. The first main purpose of the present paper is to prove this. We consider it quite important that in the necessity part of the main result of [7], the condition S = S + S can be transferred from being among the assumptions to being among the conclusions. (And in the sufficiency part, it is now clear that the assumption S = S + S is not an arbitrary one, but a necessary one.…”

Section: (X)σ (Y) Dµ(·)(ξ ξ )(σ )mentioning

confidence: 83%

Section: (X)σ (Y) Dµ(·)(ξ ξ )(σ )mentioning

confidence: 97%

“…Every R-separative finitely generated semigroup is C-finite as shown near the end of [7]. Thus, the main result of [7] (augmented by the fact that the condition S = S + S is necessary for semiperfectness) implies a characterization of semiperfect (or equivalently, completely semiperfect) R-separative finitely generated semigroups. It is the second main purpose of the present paper to extend this result to a characterization of semiperfect (or equivalently, completely semiperfect) finitely generated abelian semigroups with the identical involution.…”

Section: (X)σ (Y) Dµ(·)(ξ ξ )(σ )mentioning

confidence: 97%

“…For every * -semigroup S and for every subset V of S, denote by E(V ) the set of those v ∈ V such that if s, t ∈ S, s + s * , t + t * ∈ V , and s + t * = v then s = t. For every subset U of S, denote by C(U ) the union of all finite subsets V of S such that E(V ) ⊂ U . The semigroup S is C-finite if C(U ) is a finite set for every finite subset U of S. In [7] we included in the definition of C-finiteness the condition of R-separativity, but it is better to separate the conditions. We apologize for being inconsistent.…”

Section: (X)σ (Y) Dµ(·)(ξ ξ )(σ )mentioning

confidence: 99%

“…The main result of [7] states that a countable R-separative C-finite semigroup S satisfying S = S + S is semiperfect (or equivalently, completely semiperfect) if and only if the following condition is satisfied:…”

Section: (X)σ (Y) Dµ(·)(ξ ξ )(σ )mentioning

confidence: 99%

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Semiperfect finitely generated abelian semigroups without involution

Bisgaard¹

2002

MATH. SCAND.

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Section: (X)σ (Y) Dµ(·)(ξ ξ )(σ )mentioning

confidence: 83%

Section: (X)σ (Y) Dµ(·)(ξ ξ )(σ )mentioning

confidence: 97%

Section: (X)σ (Y) Dµ(·)(ξ ξ )(σ )mentioning

confidence: 97%

Section: (X)σ (Y) Dµ(·)(ξ ξ )(σ )mentioning

confidence: 99%

Section: (X)σ (Y) Dµ(·)(ξ ξ )(σ )mentioning

confidence: 99%

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Semiperfect finitely generated abelian semigroups without involution

Bisgaard¹

2002

MATH. SCAND.

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Cholangiocyte‐specific rat liver proteins identified by establishment of a two‐dimensional gel protein database

Tietz¹,

Groen²,

Anderson³

et al. 1998

Electrophoresis

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The liver is composed of a variety of cells that form a functional unit involved in uptake, synthesis, metabolism, and secretion. Until recently, most studies examining liver function did not analyze the specific proteins expressed or functions performed by the multiple individual cell types that constitute the hepatic mass. In the last decade, novel isolation methods have been developed that allow the purification of liver cell populations highly enriched in one type of liver cell. Here, we present a detailed two-dimensional (2-D) protein map of rat bile duct epithelial cells (i.e., cholangiocytes) using a recently developed isolation procedure. In addition, we identify 27 major cholangiocyte proteins either by comparison to maps of known rat liver proteins (based on pI and Mr) or by tryptic digestion and microsequencing. Finally, we compare the relative abundance of individual proteins present in cholangiocytes to whole liver as well as hepatocyte-specific proteins. Our results show that cholangiocytes express a unique array of individual proteins. The cholangiocyte 2-D protein pattern is markedly different from that of isolated rat hepatocytes or whole rat liver, with high levels of proteins previously known to be expressed by cholangiocytes (e.g., cytokeratins, actins) as well as protein not previously demonstrated to be expressed at high levels (e.g., annexin V, selenium binding protein). We conclude that this cholangiocyte-derived, 2-D protein map will be a crucial resource for studies directed at our understanding of cholangiocyte physiology and pathobiology.

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Pontryagin space structure in reproducing kernel Hilbert spaces over *-semigroups

Szafraniec

Wojtylak

2010

Positivity

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The geometry of spaces with indefinite inner product, known also as Krein spaces, is a basic tool for developing Operator Theory therein. In the present paper we establish a link between this geometry and the algebraic theory of * -semigroups. It goes via the positive definite functions and related to them reproducing kernel Hilbert spaces. Our concern is in describing properties of elements of the semigroup which determine shift operators which serve as Pontryagin fundamental symmetries.

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Semiperfect countable C -finite semigroups S satisfying S = S + S

Cited by 7 publications

References 0 publications

Semiperfect finitely generated abelian semigroups without involution

Semiperfect finitely generated abelian semigroups without involution

Cholangiocyte‐specific rat liver proteins identified by establishment of a two‐dimensional gel protein database

Pontryagin space structure in reproducing kernel Hilbert spaces over *-semigroups

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