Qualification:
Ph.D, MPhil
sreeja@am.amrita.edu

Dr. Sreeja V. K. obtained her Ph. D. in Mathematics from Kerala University in 2004. Her field of research was “Study of Unit Regular Semi Groups.” She had received her M. Phil. from the same university earlier in 1997. She has qualified CSIR JRF.

Dr. Sreeja has been with Amrita since 2003. She has 15 years of experience in teaching . She has published 11 research papers in international journals. She has published in the Journal of Southeast Asian Bulletin of Mathematics, Springer and has also presented papers at national conferences and seminars.

Dr. Sreeja is a recepient of the Senior Research Fellowship (SRF - 2002) and the Junior Research Fellowship (JRF - 1999) of the Council of Scientific and Industrial Research (CSIR) of India.

## Publications

### Publication Type: Journal Article

Year of Publication Title

2018

Dr. Sreeja V. K., “Construction of Inverse Unit Regular Monoids from a Semilattice and a Group”, International Journal of Engineering & Technology (UAE), vol. 7, no. 4.36, pp. 950-952, 2018.[Abstract]

This paper is a continuation of a previous paper [6] in which the structure of certain unit regular semigroups called R-strongly unit regular monoids has been studied. A monoid S is said to be unit regular if for each element s  S there exists an element u in the group of units G of S such that s = sus. Hence 1 s  suu where su is an idempotent and 1 u is a unit. A unit regular monoid S is said to be a unit regular inverse monoid if the set of idempotents of S form a semilattice. Since inverse monoids are R unipotent, every element of a unit regular inverse monoid can be written as s = eu where the idempotent part e is unique and u is a unit. Here we give a detailed study of inverse unit regular monoids and the results are mainly based on [10]. The relations between the semilattice of idempotents and the group of units in unit regular inverse monoids are better identified in this case

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2018

Dr. Sreeja V. K., “Unit Regular Inverse Monoids and Clifford Monoids (UAE)”, International journal of Engineering and Technology, vol. 7, no. 2.13, pp. 306-308, 2018.[Abstract]

Let S be a unit regular semigroup with group of units G = G(S) and semilattice of idempotents E = E(S). Then for every there is a such that Then both xu and ux are idempotents and we can write or .Thus every element of a unit regular inverse monoid is a product of a group element and an idempotent. It is evident that every L-class and every R-class contains exactly one idempotent where L and R are two of Greens relations. Since inverse monoids are R unipotent, every element of a unit regular inverse monoid can be written as s = eu where the idempotent part e is unique and u is a unit. A completely regular semigroup is a semigroup in which every element is in some subgroup of the semigroup. A Clifford semigroup is a completely regular inverse semigroup. Characterization of unit regular inverse monoids in terms of the group of units and the semilattice of idempotents is a problem often attempted and in this direction we have studied the structure of unit regular inverse monoids and Clifford monoids. More »»

2016

Dr. Sreeja V. K., “Characterization of Some Unit Regular Orthodox Submonoids of the Full Transformation Semigroup T(X)”, Southeast Asian Bulletin of Mathematics, vol. 40, no. 1, pp. 125-129, 2016.[Abstract]

. A unit regular monoid S is said to be R− strongly unit regular if for any x, y ∈ S, xRy (where R is the Green’s relation) implies that there exists an element u in the group of units of S such that x = yu. The full transformation semigroup T (X) on a finite set X is seen to be R-strongly unit regular [4]. Hence the unit regular orthodox monoid ML exist for T (X) [10]. Let G(X) denote the group of units of T (X). For a L− class L of T (X), TL is defined to be TL = ∪e∈E(L)He which is the union of the group H− classes (where E(L) denote the set of idempotents of the L− class L). Also GL is a maximal subgroup of G(X) making TL ∪ GL an unit regular orthodox monoid and ML is defined to be TL ∪ GL [10]. Here we characterize the unit regular orthodox monoid ML of T (X). In the case of T (X) we also identify the minimal subgroup G1L of G(X) which makes TL ∪ G1L an unit regular orthodox monoid. More »»

2015

Dr. Sreeja V. K. and Rajan, A. R., “Some Properties of Regular Monoids”, Southeast Asian Bulletin of Mathematics, vol. 39, pp. 891 - 902, 2015.[Abstract]

A monoid S with group of units G is said to be regular if for each x ∈ S, there is an element a ∈ S such that x = xax. We consider arbitrary monoids and describe various properties depending on the group of units. Properties of regular monoids and description of some special classes of regular monoids are also given. [ABSTRACT FROM AUTHOR]

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2015

Dr. Sreeja V. K., “Orthodox Unit Regular Submonoids of the Full Transformation Semigroup T(X)”, Southeast Asian Bulletin of Mathematics, vol. 39, pp. 711 - 715, 2015.[Abstract]

A unit regular monoid S is said to be R-strongly unit regular if for any x, y ∊ S, xRy (where R is the Green's relation implies that there exists an element u in the group of units G of S such that x = yu. The full transformation semigroup T (X) on a finite set X is seen to be R-strongly unit regular [11]. Hence the unit regular orthodox monoid QR exists for T (X) [10]. Let G(X) denote the group of units of T (X). For an R-class R of a R-strongly unit regular monoid S, ZR is defined to be ∪e∊E(R)(HG)e, where E(R) denote the set of idempotents in the R-class R and (HG)e denote the HG class containing e. (Here the equivalence HG is defined on the monoid S as xHGy if and only if x = yu and x = u'y for some unit u, u' in G.) Then QR = ZR ∪G'R (See the Remark after Theorem 1.2) is an unit regular orthodox submonoid of S. Here we characterize the unit regular orthodox monoid QR of T (X). [ABSTRACT FROM AUTHOR]

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2015

Dr. Sreeja V. K. and A.R., R., “Some combinatorial results on the full transformation semigroup”, Southeast Asian Bulletin of Mathematics, vol. 39 , no. 4, pp. 583-593, 2015.

2014

Dr. Sreeja V. K. and Rajan, A. R., “Construction of Certain Unit Regular Orthodox Submonoids”, Southeast Asian Bulletin of Mathematics, vol. 38, no. 6, pp. 907–916, 2014.[Abstract]

A regular semigroup S is said to bo orthodox if for any e, f ∈ E(S), ef ∈ E(S) where E(S) denotes the set of idempotents of S. A regular monoid S is said to be unit regular if for any x ∈ S, there exists an element u in the group of units of S such that x = xux. Here we characterize some orthodox unit regular submonoids associated with the L−class and R− class of a R−strongly (L−strongly) unit regular monoid.

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2014

Dr. Sreeja V. K., “Some Maximal Bands of the Full Transformation Semigroup”, Southeast Asian Bulletin of Mathematics, vol. 38, no. 3, pp. 445-449, 2014.[Abstract]

Bands with identity are unit regular semigroups. Moreover in a unit regular semigroup the trivial group is necessarily a band with unity. We now describe some maximal unit regular subsemigroups of the full transformation semigroup T(X) whose group of units is {1}. They are maximal subbands of T(X).

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2013

Dr. Sreeja V. K. and Rajan, A. R., “The partial strong unit regularity of the full transformation semigroup”, Southeast Asian Bulletin of Mathematics, vol. 37, no. 3, pp. 405-412, 2013.

2011

A. R. Rajan and Dr. Sreeja V. K., “CONSTRUCTION OF A R-STRONGLY UNIT REGULAR MONOID FROM A REGULAR BIORDERED SET AND A GROUP”, Asian-European Journal of Mathematics, vol. 4, pp. 653-670, 2011.[Abstract]

In this paper we give a detailed study of R-strongly unit regular monoids. The relations between the biordered set of idempotents and the group of units in unit regular semigroups are better identified here. Conversely, starting from a regular biordered set E and a group G we construct a R-strongly unit regular semigroup S for which the set of idempotents E(S) is isomorphic to E as a biordered set and the group of units G(S) is isomorphic to G. The conditions to be satisfied by G and E are also listed.

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2004

A. R. Rjan and Dr. Sreeja V. K., “Description and Counting of the Sandwich Sets in Transformation Semigroups.”, Southeast Asian Bulletin of Mathematics, vol. 27, p. 907, 2004.

## Paper Presented

Year  Title
2002 V. K. Sreeja, “R - strongly unit regular monoids”, National Seminar on Algebra and Discrete Mathematics. Department of Mathematics, University of Kerala, Kariavattom, Thiruvananthapuram
Faculty Research Interest: