Green's relations and generalized Green's relations play a fundamental role in the study of semigroups.GV-semigroups are the generalizations of completely regular semigroups in the range of π-regular semigrou...Green's relations and generalized Green's relations play a fundamental role in the study of semigroups.GV-semigroups are the generalizations of completely regular semigroups in the range of π-regular semigroups.In this paper,Green's relations and generalized Green's relations on GV-semigroups are considered by the structure of GV-semigroups.D=j and D C D* on GV-semigroups will be proved.展开更多
In this paper, we introduce the definition of （m, n）0-regularity in Г-semigroups. we in- vestigate and characterize the 20-regular class of F-semigroups using Green＇s relations. Extending and generalizing the Croi...In this paper, we introduce the definition of （m, n）0-regularity in Г-semigroups. we in- vestigate and characterize the 20-regular class of F-semigroups using Green＇s relations. Extending and generalizing the Croisot＇s Theory of Decomposition for F-semigroups, we introduce and study the absorbent and regular absorbent Г-semigroups. We approach this problem by examining quasi-ideals using Green＇s relations.展开更多
Set of integers, Z<sub>n</sub> is split into even-odd parts. The even part is arranged in ways, while the odd part fixes one point at a time to compliment the even part thereby forming the semigroup, AZ<...Set of integers, Z<sub>n</sub> is split into even-odd parts. The even part is arranged in ways, while the odd part fixes one point at a time to compliment the even part thereby forming the semigroup, AZ<sub>n</sub>. Thus, -spaces are filled choosing maximum of two even points at a time. Green’s relations have formed important structures that enhance the algebraic study of transformation semigroups. The semigroup of Alternating Nonnegative Integers for n-even (AZ<sub>n</sub><sub>-even</sub>) is shown to have only two D-classes, and there are -classes for n≥4. The cardinality of L-classes is constant. Certain cardinalities and some other properties were derived. The coefficients of the zigzag triples obtained are 1, and . The second and third coefficients can be obtained by zigzag addition.展开更多
Let ΡΥ（X） be the semigroup of all partial transformations on X, Υ（X） and Ι（X） be the subsemigroups of ΡΥ（X） of all full transformations on X and of all injective partial transformations on X, respectivel...Let ΡΥ（X） be the semigroup of all partial transformations on X, Υ（X） and Ι（X） be the subsemigroups of ΡΥ（X） of all full transformations on X and of all injective partial transformations on X, respectively. Given a non-empty subset Y of X, let ΡΥ（X, Y） = {α∈ ΡΥ（X） ： Xα Y}, Υ（X, Y） = ΡΥ（X, Y） ∩Υ（X） and Ι（X, Y） = ΡΥ（X, Y） ∩ Ι（X）. In 2008, Sanwong and Sommanee described the largest regular subsemigroup and determined Green＇s relations of Υ（X,Y）. In this paper, we present analogous results for bothΡ Υ（X, Y） and Ι（X, Y）. For a finite set X with ｜x｜≥ 3, the ranks of ΡΥ（X） = ΡΥ（X, X）, Υ（X） = Υ（X, X） and.Ι（X） = Ι（X, X） are well known to be 4, 3 and 3, respectively. In this paper, we also compute the ranks of ΡΥ（X,Y）, Υ（X, Y） and Ι（X, Y） for any proper non-empty subset Y of X.展开更多
基金Leading Academic Discipline Project of SHNU,China (No.DZL803)Innovation Project of Shanghai Education Committee,China(No.12YZ081)+2 种基金General Scientific Research Project of SHNU,China (No.SK201121)National Natural Science Foundation of China(No.11001046)Fundamental Research Fundation for the Central Universities,China (No.11D10904)
文摘Green's relations and generalized Green's relations play a fundamental role in the study of semigroups.GV-semigroups are the generalizations of completely regular semigroups in the range of π-regular semigroups.In this paper,Green's relations and generalized Green's relations on GV-semigroups are considered by the structure of GV-semigroups.D=j and D C D* on GV-semigroups will be proved.
文摘In this paper, we introduce the definition of （m, n）0-regularity in Г-semigroups. we in- vestigate and characterize the 20-regular class of F-semigroups using Green＇s relations. Extending and generalizing the Croisot＇s Theory of Decomposition for F-semigroups, we introduce and study the absorbent and regular absorbent Г-semigroups. We approach this problem by examining quasi-ideals using Green＇s relations.
文摘Set of integers, Z<sub>n</sub> is split into even-odd parts. The even part is arranged in ways, while the odd part fixes one point at a time to compliment the even part thereby forming the semigroup, AZ<sub>n</sub>. Thus, -spaces are filled choosing maximum of two even points at a time. Green’s relations have formed important structures that enhance the algebraic study of transformation semigroups. The semigroup of Alternating Nonnegative Integers for n-even (AZ<sub>n</sub><sub>-even</sub>) is shown to have only two D-classes, and there are -classes for n≥4. The cardinality of L-classes is constant. Certain cardinalities and some other properties were derived. The coefficients of the zigzag triples obtained are 1, and . The second and third coefficients can be obtained by zigzag addition.
文摘Let ΡΥ（X） be the semigroup of all partial transformations on X, Υ（X） and Ι（X） be the subsemigroups of ΡΥ（X） of all full transformations on X and of all injective partial transformations on X, respectively. Given a non-empty subset Y of X, let ΡΥ（X, Y） = {α∈ ΡΥ（X） ： Xα Y}, Υ（X, Y） = ΡΥ（X, Y） ∩Υ（X） and Ι（X, Y） = ΡΥ（X, Y） ∩ Ι（X）. In 2008, Sanwong and Sommanee described the largest regular subsemigroup and determined Green＇s relations of Υ（X,Y）. In this paper, we present analogous results for bothΡ Υ（X, Y） and Ι（X, Y）. For a finite set X with ｜x｜≥ 3, the ranks of ΡΥ（X） = ΡΥ（X, X）, Υ（X） = Υ（X, X） and.Ι（X） = Ι（X, X） are well known to be 4, 3 and 3, respectively. In this paper, we also compute the ranks of ΡΥ（X,Y）, Υ（X, Y） and Ι（X, Y） for any proper non-empty subset Y of X.
