Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2017, Cilt: 46 Sayı: 6, 1053 - 1068, 01.12.2017

Öz

Kaynakça

  • Atiyah, M. F. and Macdonald, I. G. Introduction to commutative algebra, Addison-Wesley, Reading, Mass., 1969.
  • Azarpanah, F. Intersection of essential ideals in C(X), Proc. Amer. Math. Soc. 125, 2149- 2154, 1997.
  • Azarpanah, F. and Karamzadeh, O. A. S. Algebraic characterization of some disconnected spaces, Italian. J. Pure Appl. Math. 12, 155-168, 2002.
  • Azarpanah, F., Karamzadeh, O. A. S. and Rahmati, S. C(X) VS. C(X) modulo its socle, Colloq. Math. 3, 315-336, 2008.
  • Bhattacharjee, P., Knox, M. L. and Mcgovern, W. WM. The classical ring of quotients of Cc(X), Appl. Ge Topol. 15, no. 2, 147-154, 2014.
  • Azarpanah, F., Manshoor, F. and Mohamadian, R. Connectedness and compactness in C(X) with the m-topology and generalized m-topology, Topology and its applications 159, 3486-3493, 2012.
  • Dovgoshey, O., Martio, O., Ryazanov, V. and Vuopinen, M. The Cantor function, Expo. Math. 24, 1-37, 2006.
  • Dube, T. Contracting the socle in rings of continuous functions, Rend. Semin. Mat. Univ. Padova 123, 37-53, 2010.
  • Engelking, R. General topology, Heldermann Verlag Berlin, 1989.
  • Estaji, A. A. and Karamzadeh, O. A. S. On C(X) modulo its socle, Comm. Algebra 31, 1561-1571, 2003.
  • Ganster, M. A note on strongly lindelöf spaces, Soochow J. Math. 15 (1), 99-104, 1989.
  • Ghadermazi, M., Karamzadeh, O. A. S. and Namdari, M. On the functionally countable subalgebra of C(X), Rend. Sem. Mat. Univ. Padova, 129, 47-69, 2013.
  • Ghadermazi, M., Karamzadeh, O. A. S. and Namdari, M. C(X) versus its functionally countable subalgebra, submitted in 2013.
  • Ghadermazi, M. and Namdari, M. On -scattered spaces, Far East J. Math. Sci.(FJMS), 32 (2), 267-274, 2009.
  • Ghasemzadeh, S. G., Karamzadeh, O. A. S. and Namdari, M. The super socle of the ring of continuous functions, Mathematica Slovaka, to appear.
  • Gillman, L. and Jerison, M., Rings of continuous functions, Springer-Verlag, 1976.
  • Goodearl, K. R., Von Neumann Regular Rings, Pitman, 1979.
  • Henriksen, M., Raphael, R. and Woods, R. G. SP-scattered spaces; a new generalization of scattered spaces, Comment. Math. univ. carolin 48, no. 3, 487–505, 2007.
  • Kaplansky, I. Commutative rings, Boston: Allyn and Bacon, Inc, 1970.
  • Karamzadeh, O. A. S. On a question on Matlis, Comm. Algebra, 25, 2717-2726, 1997.
  • Karamzadeh, O. A. S. and Koochakpour, A. A. On $\aleph_0$-selfinjectivity of strongly regular rings, Comm. Algebra 27, 1501-1513, 1999.
  • Karamzadeh, O. A. S. and Motamedi, M. A note on rings in which every maximal ideal is generated by a central idempotent, Proc. Japan Acad., 58 Ser. A, 124-125, 1982.
  • Karamzadeh, O. A. S., Namdari, M. and Soltanpour, S. On the locally functionally countable subalgebra of C(X), Appl. Gen. Topol., 16, no (2) 183-207, 2015.
  • Karamzadeh, O. A. S. and Rostami, M. On the intrinsic topology and some related ideals of C(X), Proc. Amer. Math. Soc. 93, 179-184, 1985.
  • Lambek, J. Lectures on rings and modules, Blaisdell, 1966.
  • Levy, R. and Rice, M.D. Normal P-spaces and the G-topology, Colloq. Math. 47, 227-240, 1981.
  • Namdari, M. and Veisi, A. The subalgebra of Cc(X) consisting of elements with countable image versus C(X) with respect to their rings of quotients, Far East J. Math. Sci. (FJMS), 59, 201-212, 2011.
  • Pelczynski, A. and Semadeni, Z. Spaces of continuous functions (III), Studia Math. 18, 211-222, 1959.
  • Rudd, D. On two sum theorems for ideals of C(X), Michigan Math. J. 17, 139-141, 1970.
  • Rudin, W. Continuous functions on compact spaces without perfect subsets, Proc. Amer. Math. Soc. 8, 39-42, 1957.
  • Rudin, M. E. and Rudin, W. Continuous functions that are locally constant on dense sets, J. Funct. Anal. 133, 120-137, 1995.
  • Willard, S. General topology, Addison-Wesley, Reading, MA, 1970.

On the locally countable subalgebra of C(X) whose local domain is cocountable

Yıl 2017, Cilt: 46 Sayı: 6, 1053 - 1068, 01.12.2017

Öz

In this paper, we present a new subring of $C(X)$ that contains the subring $C_c(X)$, the set of all continuous functions with countable image. Let $L_{cc}(X)=\{ f\in C(X)\,:\, |X\backslash C_f|\leq \aleph_0 \}$, where $C_f$ is the union of all open subsets $U\subseteq X$ such that $|f(U)|\leq \aleph_0$. We observe that $L_{cc}(X)$ enjoys most of the important properties which are shared by $C(X)$ and $C_c(X)$. It is shown that any hereditary lindel\"{o}f scattered space is functionally countable.Spaces $X$ such that $L_{cc}(X)$ is regular (von Neumann) are characterized and it is shown that $\aleph_0$-selfinjectivity and regularity of $L_{cc}(X)$ coincide.

Kaynakça

  • Atiyah, M. F. and Macdonald, I. G. Introduction to commutative algebra, Addison-Wesley, Reading, Mass., 1969.
  • Azarpanah, F. Intersection of essential ideals in C(X), Proc. Amer. Math. Soc. 125, 2149- 2154, 1997.
  • Azarpanah, F. and Karamzadeh, O. A. S. Algebraic characterization of some disconnected spaces, Italian. J. Pure Appl. Math. 12, 155-168, 2002.
  • Azarpanah, F., Karamzadeh, O. A. S. and Rahmati, S. C(X) VS. C(X) modulo its socle, Colloq. Math. 3, 315-336, 2008.
  • Bhattacharjee, P., Knox, M. L. and Mcgovern, W. WM. The classical ring of quotients of Cc(X), Appl. Ge Topol. 15, no. 2, 147-154, 2014.
  • Azarpanah, F., Manshoor, F. and Mohamadian, R. Connectedness and compactness in C(X) with the m-topology and generalized m-topology, Topology and its applications 159, 3486-3493, 2012.
  • Dovgoshey, O., Martio, O., Ryazanov, V. and Vuopinen, M. The Cantor function, Expo. Math. 24, 1-37, 2006.
  • Dube, T. Contracting the socle in rings of continuous functions, Rend. Semin. Mat. Univ. Padova 123, 37-53, 2010.
  • Engelking, R. General topology, Heldermann Verlag Berlin, 1989.
  • Estaji, A. A. and Karamzadeh, O. A. S. On C(X) modulo its socle, Comm. Algebra 31, 1561-1571, 2003.
  • Ganster, M. A note on strongly lindelöf spaces, Soochow J. Math. 15 (1), 99-104, 1989.
  • Ghadermazi, M., Karamzadeh, O. A. S. and Namdari, M. On the functionally countable subalgebra of C(X), Rend. Sem. Mat. Univ. Padova, 129, 47-69, 2013.
  • Ghadermazi, M., Karamzadeh, O. A. S. and Namdari, M. C(X) versus its functionally countable subalgebra, submitted in 2013.
  • Ghadermazi, M. and Namdari, M. On -scattered spaces, Far East J. Math. Sci.(FJMS), 32 (2), 267-274, 2009.
  • Ghasemzadeh, S. G., Karamzadeh, O. A. S. and Namdari, M. The super socle of the ring of continuous functions, Mathematica Slovaka, to appear.
  • Gillman, L. and Jerison, M., Rings of continuous functions, Springer-Verlag, 1976.
  • Goodearl, K. R., Von Neumann Regular Rings, Pitman, 1979.
  • Henriksen, M., Raphael, R. and Woods, R. G. SP-scattered spaces; a new generalization of scattered spaces, Comment. Math. univ. carolin 48, no. 3, 487–505, 2007.
  • Kaplansky, I. Commutative rings, Boston: Allyn and Bacon, Inc, 1970.
  • Karamzadeh, O. A. S. On a question on Matlis, Comm. Algebra, 25, 2717-2726, 1997.
  • Karamzadeh, O. A. S. and Koochakpour, A. A. On $\aleph_0$-selfinjectivity of strongly regular rings, Comm. Algebra 27, 1501-1513, 1999.
  • Karamzadeh, O. A. S. and Motamedi, M. A note on rings in which every maximal ideal is generated by a central idempotent, Proc. Japan Acad., 58 Ser. A, 124-125, 1982.
  • Karamzadeh, O. A. S., Namdari, M. and Soltanpour, S. On the locally functionally countable subalgebra of C(X), Appl. Gen. Topol., 16, no (2) 183-207, 2015.
  • Karamzadeh, O. A. S. and Rostami, M. On the intrinsic topology and some related ideals of C(X), Proc. Amer. Math. Soc. 93, 179-184, 1985.
  • Lambek, J. Lectures on rings and modules, Blaisdell, 1966.
  • Levy, R. and Rice, M.D. Normal P-spaces and the G-topology, Colloq. Math. 47, 227-240, 1981.
  • Namdari, M. and Veisi, A. The subalgebra of Cc(X) consisting of elements with countable image versus C(X) with respect to their rings of quotients, Far East J. Math. Sci. (FJMS), 59, 201-212, 2011.
  • Pelczynski, A. and Semadeni, Z. Spaces of continuous functions (III), Studia Math. 18, 211-222, 1959.
  • Rudd, D. On two sum theorems for ideals of C(X), Michigan Math. J. 17, 139-141, 1970.
  • Rudin, W. Continuous functions on compact spaces without perfect subsets, Proc. Amer. Math. Soc. 8, 39-42, 1957.
  • Rudin, M. E. and Rudin, W. Continuous functions that are locally constant on dense sets, J. Funct. Anal. 133, 120-137, 1995.
  • Willard, S. General topology, Addison-Wesley, Reading, MA, 1970.
Toplam 32 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

R. Mehri Bu kişi benim

R. Mohamadian Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 46 Sayı: 6

Kaynak Göster

APA Mehri, R., & Mohamadian, R. (2017). On the locally countable subalgebra of C(X) whose local domain is cocountable. Hacettepe Journal of Mathematics and Statistics, 46(6), 1053-1068.
AMA Mehri R, Mohamadian R. On the locally countable subalgebra of C(X) whose local domain is cocountable. Hacettepe Journal of Mathematics and Statistics. Aralık 2017;46(6):1053-1068.
Chicago Mehri, R., ve R. Mohamadian. “On the Locally Countable Subalgebra of C(X) Whose Local Domain Is Cocountable”. Hacettepe Journal of Mathematics and Statistics 46, sy. 6 (Aralık 2017): 1053-68.
EndNote Mehri R, Mohamadian R (01 Aralık 2017) On the locally countable subalgebra of C(X) whose local domain is cocountable. Hacettepe Journal of Mathematics and Statistics 46 6 1053–1068.
IEEE R. Mehri ve R. Mohamadian, “On the locally countable subalgebra of C(X) whose local domain is cocountable”, Hacettepe Journal of Mathematics and Statistics, c. 46, sy. 6, ss. 1053–1068, 2017.
ISNAD Mehri, R. - Mohamadian, R. “On the Locally Countable Subalgebra of C(X) Whose Local Domain Is Cocountable”. Hacettepe Journal of Mathematics and Statistics 46/6 (Aralık 2017), 1053-1068.
JAMA Mehri R, Mohamadian R. On the locally countable subalgebra of C(X) whose local domain is cocountable. Hacettepe Journal of Mathematics and Statistics. 2017;46:1053–1068.
MLA Mehri, R. ve R. Mohamadian. “On the Locally Countable Subalgebra of C(X) Whose Local Domain Is Cocountable”. Hacettepe Journal of Mathematics and Statistics, c. 46, sy. 6, 2017, ss. 1053-68.
Vancouver Mehri R, Mohamadian R. On the locally countable subalgebra of C(X) whose local domain is cocountable. Hacettepe Journal of Mathematics and Statistics. 2017;46(6):1053-68.