A semigroup S is J -trivial if any two distinct elements of S must
generate distinct ideals of S. We investigate this condition for the semigroup
of all right ideals of a ring under right ideal multiplication. There is a rich interplay
between the underlying ring and the semigroup of all of its right ideals.
G. F. Birkenmeier, Idempotents and completely semiprime ideals, Comm. Al- gebra, 11 (1983), 567–580.
B. Brown and N. H. McCoy, Rings with unit element which contain a given ring, Duke Math. J., 13 (1956), 9–20.
A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups, Vol. I, Mathematical Surveys of the American Mathematical Society no.7, Providence, R. I., 1961.
N. Divinsky, Rings and Radicals, Univ. Toronto Press, Toronto, 1965.
J,. L. Dorroh, Concerning adjunctions to algebras, Bull. Amer. Math. Soc., 38 (1932), 85–88.
K. R. Goodearl, Von Neumann Regular Rings, Pitman, London, 1979.
H. E. Heatherly and R. P. Tucci, The semigroup of right ideals of a ring, Math. Pannon., 18(1) (2007), 19–26.
H. E. Heatherly, K. A. Kosler, and R. P. Tucci, Semigroups of ideals of right weakly regular ring, JP J. Algebra Number Theory Appl., 15 (2009), 89–100.
H. E. Heatherly and R. P. Tucci, Right weakly regular rings: A Survey, in Ring and Module Theory by T. Albu, G. F. Birkenmeier, A. Erdo˘gan, and A. Tercan, eds., Springer Verlag Trends in Mathematics 2010, Basel, 115–124.
S. K. Jain and S. Jain, Restricted regular rings, Math. Z., 121 (1971), 51–54.
A. Kert´esz, Lectures on Artinian Rings, Akademiai Kiado, Budapest, 1987.
J. E. Pin, Varieties of Formal Languages, Plenum Press, New York, 1986.
T. Saito,J -trivial subsemigroups of finite full transformation semigroups, Semigroup Forum, 57 (1998), 60–68.
A. Smoktunowicz, A simple nil ring exists, Comm. Algebra, 30 (2002), 27–59.
F. A. Szasz, Radicals of Rings, John Wiley and Sons, New York, 1981.
A. Tuganbaev, Rings Close to Regular, Kluwer Academic Publ., Dordrecht, The Netherlands, 2002. Henry E. Heatherly
Department of Mathematics University of Louisiana at Lafayette Lafayette, Louisiana 70504 e-mail: heh5820@louisiana.edu Ralph P. Tucci
Department of Mathematical Sciences Loyola University New Orleans New Orleans, LA. 70118 e-mail: tucci@loyno.edu
Year 2011,
Volume: 10 Issue: 10, 151 - 161, 01.12.2011
G. F. Birkenmeier, Idempotents and completely semiprime ideals, Comm. Al- gebra, 11 (1983), 567–580.
B. Brown and N. H. McCoy, Rings with unit element which contain a given ring, Duke Math. J., 13 (1956), 9–20.
A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups, Vol. I, Mathematical Surveys of the American Mathematical Society no.7, Providence, R. I., 1961.
N. Divinsky, Rings and Radicals, Univ. Toronto Press, Toronto, 1965.
J,. L. Dorroh, Concerning adjunctions to algebras, Bull. Amer. Math. Soc., 38 (1932), 85–88.
K. R. Goodearl, Von Neumann Regular Rings, Pitman, London, 1979.
H. E. Heatherly and R. P. Tucci, The semigroup of right ideals of a ring, Math. Pannon., 18(1) (2007), 19–26.
H. E. Heatherly, K. A. Kosler, and R. P. Tucci, Semigroups of ideals of right weakly regular ring, JP J. Algebra Number Theory Appl., 15 (2009), 89–100.
H. E. Heatherly and R. P. Tucci, Right weakly regular rings: A Survey, in Ring and Module Theory by T. Albu, G. F. Birkenmeier, A. Erdo˘gan, and A. Tercan, eds., Springer Verlag Trends in Mathematics 2010, Basel, 115–124.
S. K. Jain and S. Jain, Restricted regular rings, Math. Z., 121 (1971), 51–54.
A. Kert´esz, Lectures on Artinian Rings, Akademiai Kiado, Budapest, 1987.
J. E. Pin, Varieties of Formal Languages, Plenum Press, New York, 1986.
T. Saito,J -trivial subsemigroups of finite full transformation semigroups, Semigroup Forum, 57 (1998), 60–68.
A. Smoktunowicz, A simple nil ring exists, Comm. Algebra, 30 (2002), 27–59.
F. A. Szasz, Radicals of Rings, John Wiley and Sons, New York, 1981.
A. Tuganbaev, Rings Close to Regular, Kluwer Academic Publ., Dordrecht, The Netherlands, 2002. Henry E. Heatherly
Department of Mathematics University of Louisiana at Lafayette Lafayette, Louisiana 70504 e-mail: heh5820@louisiana.edu Ralph P. Tucci
Department of Mathematical Sciences Loyola University New Orleans New Orleans, LA. 70118 e-mail: tucci@loyno.edu
Heatherly, H. E., & Tucci, R. P. (2011). RINGS WHOSE SEMIGROUP OF RIGHT IDEALS IS J -TRIVIAL. International Electronic Journal of Algebra, 10(10), 151-161.
AMA
Heatherly HE, Tucci RP. RINGS WHOSE SEMIGROUP OF RIGHT IDEALS IS J -TRIVIAL. IEJA. December 2011;10(10):151-161.
Chicago
Heatherly, Henry E., and Ralph P. Tucci. “RINGS WHOSE SEMIGROUP OF RIGHT IDEALS IS J -TRIVIAL”. International Electronic Journal of Algebra 10, no. 10 (December 2011): 151-61.
EndNote
Heatherly HE, Tucci RP (December 1, 2011) RINGS WHOSE SEMIGROUP OF RIGHT IDEALS IS J -TRIVIAL. International Electronic Journal of Algebra 10 10 151–161.
IEEE
H. E. Heatherly and R. P. Tucci, “RINGS WHOSE SEMIGROUP OF RIGHT IDEALS IS J -TRIVIAL”, IEJA, vol. 10, no. 10, pp. 151–161, 2011.
ISNAD
Heatherly, Henry E. - Tucci, Ralph P. “RINGS WHOSE SEMIGROUP OF RIGHT IDEALS IS J -TRIVIAL”. International Electronic Journal of Algebra 10/10 (December 2011), 151-161.
JAMA
Heatherly HE, Tucci RP. RINGS WHOSE SEMIGROUP OF RIGHT IDEALS IS J -TRIVIAL. IEJA. 2011;10:151–161.
MLA
Heatherly, Henry E. and Ralph P. Tucci. “RINGS WHOSE SEMIGROUP OF RIGHT IDEALS IS J -TRIVIAL”. International Electronic Journal of Algebra, vol. 10, no. 10, 2011, pp. 151-6.
Vancouver
Heatherly HE, Tucci RP. RINGS WHOSE SEMIGROUP OF RIGHT IDEALS IS J -TRIVIAL. IEJA. 2011;10(10):151-6.