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Adhikari, M R
- On Maximal K- Ideals of Semirings
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Authors
Affiliations
1 Department of Mathematics University of Burdwan 713104. West Bengal, IN
2 Department of Mathematics, S S Mahavidyalaya, Ajodhya, Howrah, IN
1 Department of Mathematics University of Burdwan 713104. West Bengal, IN
2 Department of Mathematics, S S Mahavidyalaya, Ajodhya, Howrah, IN
Source
Indian Science Cruiser, Vol 9, No 3 (1995), Pagination: 23-30Abstract
The k- ideals of semirings were investigated by M K Sen and M R Adhikari' I In this paper, for a semiring S with commutative addition, conditions are considered such that S has non-trivial h-ideals or maximal h-ideals, among others by the help of lizuka Congruence class semiring S/A defined by an ideal A of S. Moreover, semirings with descending chain conditions are studied.Keywords
Semirings, k-ideal, h-ideal. Bourne Congruence and lizuka congruence
References
- M K Sen and M R Adhikari, On k-ideals of stmmngs, Jnternationat J of Math and Math Sciences (USA), 15 (2), 347-350, 1992.
- M K Sen and M R Adhikari, On maximal k-ideals of semirings, Proc Amer Math Soc. 118(3), 699-703, 1993.
- H J Weinert, Uber Halbringe and Halbkorperl, ACTA Math Acad Sc Hunger, 13, 365-378, 1962.
- M Henriksen, Ideals in semirings with commulative addition, Amer Math Soc Notices 5, 321, 1958.
- K lizuka, On the Jacobson radical of a semiring, Tohoku Math J 11(2); 409-421, 1959.
- S Bourne, The Jacobson radical of a semiring, Proc Nat Acad Sci (USA) 37, 169-170, 1951.
- S Bourne and H Zassenhaus, On the radicals of a semiring, Proc Nat Acad Sci, 44, 907-914, 1958.
- D R Latorre, On h-idea!s and k-ideals in hemirings. Pub Math Debrecen, 14, 9-13, 1967.
- M R Adhikari and M K Sen, Cohen's Theorem for a class of semirings, Indian Sc Cr 9(1), 28-33, 1995.
- M K Sen and M R Adhikari, On division hemirings. Bull Cal Math Soc, 83, 267-274, 1991.
- M R Adhikari, Groups, rings and semirings with applications (In Press).
- On Peripheral Connectedness
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Authors
M K Das
1,
M R Adhikari
2
Affiliations
1 S N Bose School of Mathematics and Mathematical Physics, Calcutta Mathematical Society, Calcutta, West Bengal, IN
2 Department of Mathematics, Burdwan University, Burdwan, West Bengal, IN
1 S N Bose School of Mathematics and Mathematical Physics, Calcutta Mathematical Society, Calcutta, West Bengal, IN
2 Department of Mathematics, Burdwan University, Burdwan, West Bengal, IN
Source
Indian Science Cruiser, Vol 6, No 1 (1992), Pagination: 24-26Abstract
Rote' ha.s proved that if the locally compact, metric space X is peripherically cohomologically locally connected, then X is peripherically homologicully locally connected. However the converse has been proved by him assuming that X is homologically locally connected. In this note we prove the above conver.se in .some general casesKeywords
Peripherically Homologically and Cohomologically Locally Connected Spaces, Homologically Locally Connected SpacesReferences
- D Role, Peripherical Cohomologieal Local Connectedness, Fund Math, Vol 116, No 1, p 53-66, 1983.
- EH Spainer, Algebraic Topology, McGraw-Hill, 1966.
- E G Sklyarenko, Homology Theory and Exactness Axoim, Uspekhi Math N, Vol 19, No 6, p 47-70, 1964.
- A E Harlap, Local Homology and Cohomology, Homology Dimension and Generalised Manifold, Mat Sb, Vol 96, No 3, p 347-372, 1975.