On Le- Ternary Semi Groups-II
C. Sreemannarayana1, D. Madhusudhana Rao2, P. Sivaprasad3, M. Sajani Lavanya4, K. Anuradha5
1C. Sreemannarayana, Research Scholar, Department of Mathematics, KL University, Vaddeswaram, Guntur (A.P), India.
2D. Madhusudhana Rao, Department of Mathematics, VSR & NVR College, Tenali, Guntur (A.P), India.
3P. Sivaprasad, Department of BSH, VFSTR’S University, Vadlamudi, Guntur (A.P), India.
4M. Sajani Lavanya, Department of Mathematics, AC College, Guntur (A.P), India.
5K. Anuradha, Department of Mathematics, Andhra Loyola College, Vijayawada (A.P), India.
Manuscript received on 28 February 2019 | Revised Manuscript received on 14 March 2019 | Manuscript Published on 17 March 2019 | PP: 168-170 | Volume-7 Issue-ICETESM18, March 2019 | Retrieval Number: ICETESM38|19©BEIESP
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: The ternary semi group of all bi-ties (K) of le-ternary semi group K is a band iff K is both regular as well as intraregular. Here, we show (K) is a band iff it is normal band. Our main aim to prove (1) Suppose K be an le-ternary semi group. Then (K)(K)ℜ(K) ⊆ (k). Moreover, K is regular, then (k) = (K)(K)ℜ(K). (2) Let K is a regular le-ternary semi group. Then (K), (K), &ℜ(K) are bands. (3) An le-ternary semi group K is regular as well as intraregular iff (k) is a band (4) Suppose that K be an le-ternary semi group. Then K is both regular as well as intraregular iff (k) is a normal band. (5) An le-ternary semi group K is left duo iff kle ≤ lek ≤ ekl for all k, l ∈ K (6) An le-ternary semi group K is duo iff kle = lek = ekl for all k, l ∈ K. (7) An le-ternary semi group K is regular left duo iff (k) is a left normal band. (8) An le-ternary semi group K is regular right duo iff (k) is a right normal band. Mathematical Subject Classification: 06F99, 06F05, 20M10.
Keywords: Duo, Regular, Bi-Ideal Element, Intra-Regular, Locally Testable, Normal Band, and Regular.
Scope of the Article: Cryptography and Applied Mathematics