On k-radicals of Green's relations in semirings with a semilattice additive reduct

Tapas Kumar Mondal; Anjan Kumar Bhuniya

Discussiones Mathematicae - General Algebra and Applications (2013)

  • Volume: 33, Issue: 1, page 85-93
  • ISSN: 1509-9415

Abstract

top
We introduce the k-radicals of Green's relations in semirings with a semilattice additive reduct, introduce the notion of left k-regular (right k-regular) semirings and characterize these semirings by k-radicals of Green's relations. We also characterize the semirings which are distributive lattices of left k-simple subsemirings by k-radicals of Green's relations.

How to cite

top

Tapas Kumar Mondal, and Anjan Kumar Bhuniya. "On k-radicals of Green's relations in semirings with a semilattice additive reduct." Discussiones Mathematicae - General Algebra and Applications 33.1 (2013): 85-93. <http://eudml.org/doc/270491>.

@article{TapasKumarMondal2013,
abstract = {We introduce the k-radicals of Green's relations in semirings with a semilattice additive reduct, introduce the notion of left k-regular (right k-regular) semirings and characterize these semirings by k-radicals of Green's relations. We also characterize the semirings which are distributive lattices of left k-simple subsemirings by k-radicals of Green's relations.},
author = {Tapas Kumar Mondal, Anjan Kumar Bhuniya},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {k-radicals of Green's relations; left k-regular semiring; left k-simple semiring; distributive lattices of left k-simple semirings; -radicals; Green relations; left -regular semirings; distributive lattices of left -simple semirings; semilattice additive reducts},
language = {eng},
number = {1},
pages = {85-93},
title = {On k-radicals of Green's relations in semirings with a semilattice additive reduct},
url = {http://eudml.org/doc/270491},
volume = {33},
year = {2013},
}

TY - JOUR
AU - Tapas Kumar Mondal
AU - Anjan Kumar Bhuniya
TI - On k-radicals of Green's relations in semirings with a semilattice additive reduct
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2013
VL - 33
IS - 1
SP - 85
EP - 93
AB - We introduce the k-radicals of Green's relations in semirings with a semilattice additive reduct, introduce the notion of left k-regular (right k-regular) semirings and characterize these semirings by k-radicals of Green's relations. We also characterize the semirings which are distributive lattices of left k-simple subsemirings by k-radicals of Green's relations.
LA - eng
KW - k-radicals of Green's relations; left k-regular semiring; left k-simple semiring; distributive lattices of left k-simple semirings; -radicals; Green relations; left -regular semirings; distributive lattices of left -simple semirings; semilattice additive reducts
UR - http://eudml.org/doc/270491
ER -

References

top
  1. [1] A.K. Bhuniya, On the additively regular semirings, Ph.D Thesis, University of Calcutta, 2009. 
  2. [2] A.K. Bhuniya and K. Jana, Bi-ideals in k-regular and intra k-regular semirings, Discuss. Math. General Algebra and Applications 31 (2011) 5-25. ISSN 2084-0373 Zbl1254.16040
  3. [3] A.K. Bhuniya and T.K. Mondal, Distributive lattice decompositions of semirings with a semilattice additive reduct, Semigroup Forum 80 (2010) 293-301. doi: 10.1007/s00233-009-9205-6 Zbl1205.16039
  4. [4] A.K. Bhuniya and T.K. Mondal, Semirings which are distributive lattices of left k-Archimedean semirings, Semigroup Forum (to appear). ISSN 1432-2137 Zbl1274.16066
  5. [5] A.K. Bhuniya and T.K. Mondal, Semirings which are distributive lattices of k-simple semirings, Southeast Asian Bulletin of Mathematics 36 (2012) 309-318. ISSN 0129-2021 Zbl1274.16066
  6. [6] S. Bogdanović and M. Ćirić, A note on radicals of Green's relations, PU.M.A 7 (1996) 215-219. ISSN 1218-4586 Zbl0880.20045
  7. [7] S. Bogdanović and M. Ćirić, A note on left regular semigroups Publ. Math. Debrecen 48 (3-4) (1996) 285-291. ISSN 0033-3883 Zbl1259.20063
  8. [8] A.H. Clifford and G.B. Preston, The algebraic theory of semigroups I, Amer. Math. Soc., 1977. ISBN 0-8218-0271-2 
  9. [9] A.H. Clifford, Semigroups admitting relative inverses, Ann. Math. 42 (1941) 1037-1049. ISSN 1939-0980 Zbl0063.00920
  10. [10] U. Hebisch and H.J. Weinert, Semirings. Algebraic Theory and Applications in Computer Science (Singapore, World Scientific, 1998). ISBN 981-02-3601-8 Zbl0934.16046
  11. [11] J.M. Howie, Fundamentals of semigroup theory (Clarendon, Oxford, 1995). Reprint in 2003. ISBN 0-19-851194-9 Zbl0835.20077
  12. [12] G.L. Litvinov and V.P. Maslov, The Correspondence principle for idempotent calculus and some computer applications, in: Idempotency, J. Gunawardena (Editor), (Cambridge, Cambridge Univ. Press, 1998) 420-443. Zbl0897.68050
  13. [13] G.L. Litvinov, V.P. Maslov and A.N. Sobolevskii, Idempotent Mathematics and Interval Analysis, Preprint ESI 632, The Erwin Schrödinger International Institute for Mathematical Physics, Vienna, 1998; e-print: http://www.esi.ac.at and http://arXiv.org,math.Sc/9911126. 
  14. [14] T.K. Mondal, Distributive lattices of t-k-Archimedean semirings, Discuss. Math. General Algebra and Applications 31 (2011), 147-158. doi: 10.7151/dmgaa.1179 Zbl1254.16042
  15. [15] T.K. Mondal and A.K. Bhuniya, Semirings which are distributive lattices of t-k-simple semirings, submitted. Zbl1274.16066
  16. [16] M.K. Sen and A.K. Bhuniya, On semirings whose additive reduct is a semilattice, Semigroup forum 82 (2011) 131-140. doi: 10.1007/s00233-010-9271-9 Zbl1248.16038
  17. [17] L.N. Shevrin, Theory of epigroups I, Mat. Sbornic 185 (8) (1994) 129-160. ISSN 1468-4802 Zbl0839.20073
  18. [18] H.S. Vandiver, Note on a simple type of algebra in which the cancellation law of addition does not hold, Bull. Amer. Math. Soc. 40 (1934) 914-920. ISSN 1088-9485 Zbl0010.38804

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.