scholarly journals A nilpotent-generated semigroup associated with a semigroup of full transformations

1988 ◽  
Vol 108 (1-2) ◽  
pp. 181-187 ◽  
Author(s):  
John M. Howie ◽  
M. Paula O. Marques-Smith
Keyword(s):  
Regular Cardinal ◽  
Principal Factor ◽  
Nilpotent Elements ◽  
Index 2 ◽  
Stable Elements ◽  
Regular Cardinality

SynopsisLet X be a set with infinite regular cardinality m and let ℱ(X) be the semigroup of all self-maps of X. The semigroup Qm of ‘balanced’ elements of ℱ(X) plays an important role in the study by Howie [3,5,6] of idempotent-generated subsemigroups of ℱ(X), as does the subset Sm of ‘stable’ elements, which is a subsemigroup of Qm if and only if m is a regular cardinal. The principal factor Pm of Qm, corresponding to the maximum ℱ-class Jm, contains Sm and has been shown in [7] to have a number of interesting properties.Let N2 be the set of all nilpotent elements of index 2 in Pm. Then the subsemigroup (N2) of Pm generated by N2 consists exactly of the elements in Pm/Sm. Moreover Pm/Sm has 2-nilpotent-depth 3, in the sense that

Nilpotent local automorphisms of an independence algebra

1994 ◽  
Vol 124 (3) ◽  
pp. 423-436 ◽  
Author(s):  
Lucinda M. Lima
Keyword(s):  
Positive Integer ◽  
Inverse Monoid ◽  
Nilpotent Elements ◽  
Infinite Rank ◽  
Index 2

Let A be a strong independence algebra of infinite rank m. Let ℒ(A) be the inverse monoid of all local automorphisms of A. The Baer–Levi semigroup B over the algebra A is defined to be the subsemigroup of ℒ(A) consisting of all the elements α with dom α = A and corank im α = m. Let Km be the subsemigroup of ℒ(A) generated by B−1B. Then Km is inverse and it is generated (as a semigroup) by N2, the subset of ℒ(A) consisting of all nilpotent elements of index 2. The 2-nilpotent depth, Δ2(Km) of Km is defined to be the smallest positive integer t such that Km = N2∪…∪(N2)t. In fact, Δ2(Km) is either 2 or 3 and a criterion is found which distinguishes between the two cases.If N denotes the set of all nilpotents in ℒ(A), then the subsemigroup generated by N is also Km. In fact, Km is proved to be exactly N2.

scholarly journals Inverse semigroups generated by nilpotent transformations

1984 ◽  
Vol 99 (1-2) ◽  
pp. 153-162 ◽  
Author(s):  
John M. Howie ◽  
M. Paula O. Marques-Smith
Keyword(s):  
Inverse Semigroup ◽  
Homomorphic Image ◽  
Inverse Semigroups ◽  
Nilpotent Elements ◽  
Inverse Subsemigroup ◽  
Symmetric Inverse Semigroup ◽  
Infinite Cardinality ◽  
Index 2 ◽  
Rees Quotient ◽  
The Ideal

SynopsisLet X be a set with infinite cardinality m and let B be the Baer-Levi semigroup, consisting of all one-one mappings a:X→X for which ∣X/Xα∣ = m. Let Km=<B 1B>, the inverse subsemigroup of the symmetric inverse semigroup ℐ(X) generated by all products β−γ, with β,γ∈B. Then Km = <N2>, where N2 is the subset of ℐ(X) consisting of all nilpotent elements of index 2. Moreover, Km has 2-nilpotent-depth 3, in the sense that Let Pm be the ideal {α∈Km: ∣dom α∣<m} in Km and let Lm be the Rees quotient Km/Pm. Then Lm is a 0-bisimple, 2-nilpotent-generated inverse semigroup with 2-nilpotent-depth 3. The minimum non-trivial homomorphic image of Lm also has these properties and is congruence-free.

On quasi-radical of near-ring of polynomials

2019 ◽  
Vol 56 (2) ◽  
pp. 252-259
Author(s):  
Ebrahim Hashemi ◽  
Fatemeh Shokuhifar ◽  
Abdollah Alhevaz
Keyword(s):  
Commutative Ring ◽  
Nilpotent Elements ◽  
Ring Of Polynomials

Abstract The intersection of all maximal right ideals of a near-ring N is called the quasi-radical of N. In this paper, first we show that the quasi-radical of the zero-symmetric near-ring of polynomials R0[x] equals to the set of all nilpotent elements of R0[x], when R is a commutative ring with Nil (R)2 = 0. Then we show that the quasi-radical of R0[x] is a subset of the intersection of all maximal left ideals of R0[x]. Also, we give an example to show that for some commutative ring R the quasi-radical of R0[x] coincides with the intersection of all maximal left ideals of R0[x]. Moreover, we prove that the quasi-radical of R0[x] is the greatest quasi-regular (right) ideal of it.

Prevalencia de lesiones no cariosas que causan hipersensibilidad en pacientes de la Clínica Odontológica Pasto

2017 ◽  
Vol 7 (19) ◽  
pp. 25
Author(s):  
Ximena Andrea Cerón ◽  
Richard Fernando Narvaez ◽  
Andrea Elizaberh Madroñero ◽  
Lisbeth Soffía Chavez ◽  
Angela Stefanía Tobar
Keyword(s):  
Principal Factor

Objetivo. El propósito de este estudio fue identificar la prevalencia de lesiones no cariosas que causan hipersensibilidad dentinaria. Métodos. El estudio fue de tipo descriptivo transversal, estuvo conformado por 180 pacientes con hipersensibilidad que asistían a la Clínica Odontológica en el periodo 2013 a 2014, de los cuales 65 presentaron lesiones no cariosas asociadas a hipersensibilidad, se incluyeron pacientes con lesiones no cariosas tipo abrasión, erosión y abfracción y se excluyeron pacientes con caries, restauraciones extensas y compromiso periapical, para la medición del grado de hipersensibilidad se utilizó  la clasificación de Chadwick y Mason. Resultados. Para el análisis de resultados, se utilizó el programa SPSS V.20, y para la asociación de variables y factor de riesgo se tomó como referencia la medida Chi-cuadrado. Se observó que la hipersensibilidad se presentó más en el grupo de edad de 15 a 24 años (43 %), siendo mayor en el género femenino (55,6 %), se presentó con mayor frecuencia la hipersensibilidad grado1 (50 %) y recesión clase I (37,8 %), la lesión no cariosa con mayor número de casos fue la abrasión (49,2 %). Se obtuvo resultados significativos con la prueba Chi cuadrado de Pearson (p<0.05), entre el consumo de jugos cítricos asociados a recesión y erosión. Respecto a la variable edad se encontró significancia con las lesiones abrasión, erosión y consumo de jugos cítricos (p<0.05). Conclusiones. Existió relación significativa entre el consumo de jugos cítricos como principal factor de riesgo de presentar lesiones como erosión y recesión.

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