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 12 years of experience in teaching . She has published 9 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

Publication Type

Title

2016

Journal Article

V. K. Sreeja, “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.
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2015

Journal Article

V. K. Sreeja 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.

2015

Journal Article

V. K. Sreeja, “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]

V. K. Sreeja 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]

V. K. Sreeja, “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).

V. K. Sreeja 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.

V. K. Sreeja 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

Journal Article

A. R. Rajan and 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

Journal Article

A. R. Rjan and 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

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 12 years of experience in teaching . She has published 9 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

. 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 »»

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]

More »»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]

More »»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).

More »»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.

More »»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. More »»

## Paper Presented

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