H-coextension of the double four spiral semigroup Dsp4

다국어 초록 (Multilingual Abstract)

In 1978, Byleen, Meakin and Pastijn[2,3] introduced the four - spiral semigroup Sp4 and the double four-spiral semigroup DSp4 and studied their semigroup Sp4 and studied their properties in detail. These regular semigroups play an important role in the theory of idempotent generated bismple but not completely simple semigroups. The semigroup A(1, 2) was introduced as a tool to analyse the structure of DSp4 [3]. In 2003, Chandrasekaran and Loganathan[7] observed that A(1, 2) has an inverse transveral which is a bicyclic monoid and applied this fact to represent DSp4 as a regular Rees matrix semigroup over A(1,2). This result is analogous to the representation due to Byleen [1] of the fundamental four spiral semigroup analogous to Reilly`s description of the bisimple-w-semigroups[21]. So it is natural to ask the following question. Determine the H-coextension of the R-unipotent semigroup A(1, 2) and then we describe the H-coextension of the double four spiral semigroup DSp4.

참고문헌 (Reference)

1 W.D.Munn, "The idempotent separating congruence on a regular 0-bisimple semigroup" 15 : 233-240, 1967

2 K.Byleen, "The fundamental four-spiral semigroup, Simon Stevin" 54 : 6-26, 1978

3 K.Byleen, "The double four-spiral semigroup" 54 : 75-105, 1980

4 V.M.Chandrasekaran, "Structure of the Double Four-spiral Semigroup" 경북대학교 자연과학대학 수학과 43 (43): 503-512, 2003

5 K.S.S.Nambooripad, "Structure of regular semigroups I" 22 (22): 1979

6 K.Indhira, "Structure of regular semigroup with a regular idempotent" 6 (6): 557-570, 2011

7 V.M.Chandrasekaran, "Structure of coextensions of regular semigroups by rectangular bands" 12 (12): 261-266, 2003

8 J.Meakin, "Structure mapping coextension and regular four-spiral semigroups" 225 : 111-134, 1979

9 V.M.Chandrasekaran, "Split map and idempotent separating congruence" 18 (18): 351-360, 2005

10 T.E.Hall, "Some properties of local subsemigroups inherited by larger subsemigroups" 25 : 35-49, 1982

11 M.Loganathan, "Regular semigroups with a split map" 44 : 199-212, 1992

12 M.Loganathan, "Regular semigroups with a medial idempotent" 36 : 69-74, 1987

13 T.S.Blyth, "Regular semigroup with a multiplicative inverse transversal" 92A : 253-270, 1982

14 K.Byleen, "Regular four-spiral semigroups, idempotent generated semigroups and the Rees Construction" 22 : 97-100, 1981

15 K.Indhira, "Idempotent separating congruence on a regular semigroup with a regular idempotent" 7 (7): 107-114, 2013

16 T.E.Hall, "Congruences and Green’s relations on regular semigroups" 13 : 167-175, 1972

17 M.Loganathan, "Complementation and inner automorphism for regular semigroups" 21 : 195-204, 1980

18 J.Meakin, "Coextensions of regular semigroups by rectangular bands I" 269 (269): 197-224, 1982

19 Reilly, "Bisimple w-semigroups" 7 : 160-167, 1966

20 J.M.Howie, "An introduction to semigroup theory" Academic press 1976

21 K.Indhira, "A study on some special classes of regular semigroups" VIT University 2011