Content Semimodules
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Abstract
The purpose of this paper is to study content semimodules. We obtain some results on content semimodules similar to the corresponding ones on content modules. We study normally flat content semimodules and multiplication content semimodules. Moreover, we characterize content semimodules over discrete valuation semirings and Boolean algebras.
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How to Cite
Razavi Nazari, R., & Ghalandarzadeh, S. (2017). Content Semimodules. Extracta Mathematicae, 32(2), 239-254. Retrieved from https://publicaciones.unex.es/index.php/EM/article/view/2605-5686.32.2.239
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Section
Asociative Rings and Algebras
References
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Y. Katsov, T.G. Nam, N.X. Tuyen, On subtractive semisimple semirings, Algebra Colloq. 16 (3) (2009), 415 – 426.
P. Nasehpour, On the content of polynomials over semirings and its applications, J. Algebra Appl. 15 (5) (2016), 1650088.
P. Nasehpour, Valuation semirings, J. Algebra Appl. 16 (11) (2018), 1850073.
J. Ohm, D. Rush, Content modules and algebras, Math. Scand. 31 (1972), 49 – 68.
B. Pareigis, H. Rohrl, Remarks on semimodules, arXiv: 1305.5531, 2013.
R. Razavi Nazari, Sh. Ghalandarzadeh, Multiplication semimodules, submitted.
H. Subramanian, Von Neumann regularity in semirings, Math. Nachr. 45 (1970), 73 – 79.
M. Shabir, “Some Characterizations and Sheaf Representations of Regular and Weakly Regular Monoids and Semirings”, PhD Thesis, Quaid-I-Azam University, Pakistan, 1995.
G. Yesilot, K. Orel, U. Tekir, On prime subsemimodules of semimodules, Int. J. Algebra 4 (1) (2010), 53 – 60.
J.Y. Abuhlail, Some remarks on tensor products and flatness of semimodules, Semigroup Forum 88 (3) (2014), 732 – 738.
H.M.J. Al-Thani, Characterizations of projective and k-projective semimodules,Int. J. Math. Math. Sci. 32 (7) (2002), 439 – 448.
N. Bourbaki, “Commutative Algebra”, Hermann/Addison-Wesley, 1972.
R. Ebrahimi Atani, S. Ebrahimi Atani, On subsemimodules of semi- modules, Bul. Acad. Ştiinţe Repub. Mold. Mat. 2 (63) (2010), 20 – 30.
Z.A. El-Bast, P.F. Smith, Multiplication modules, Comm. Algebra 16 (4) (1988), 755 – 779.
K. Glazek, “A Guide to the Literature on Semirings and Their Applications in Mathematics and Information Sciences”, Kluwer Academic Publishers, Dordrecht, 2002.
J.S. Golan, “Semirings and Their Applications”, Kluwer Academic Publishers, Dordrecht, 1999.
U. Hebisch, H.J. Weinert, “Semirings-Algebraic Theory and Applications in Computer Science”, World Scientific Publishing Co., Singapore, 1998.
Y. Katsov, Toward homological characterization of semirings: Serre’s conjecture and Bass’s perfectness in a semiring context, Algebra Universalis 52 (2) (2004), 197 – 214.
Y. Katsov, T.G. Nam, N.X. Tuyen, On subtractive semisimple semirings, Algebra Colloq. 16 (3) (2009), 415 – 426.
P. Nasehpour, On the content of polynomials over semirings and its applications, J. Algebra Appl. 15 (5) (2016), 1650088.
P. Nasehpour, Valuation semirings, J. Algebra Appl. 16 (11) (2018), 1850073.
J. Ohm, D. Rush, Content modules and algebras, Math. Scand. 31 (1972), 49 – 68.
B. Pareigis, H. Rohrl, Remarks on semimodules, arXiv: 1305.5531, 2013.
R. Razavi Nazari, Sh. Ghalandarzadeh, Multiplication semimodules, submitted.
H. Subramanian, Von Neumann regularity in semirings, Math. Nachr. 45 (1970), 73 – 79.
M. Shabir, “Some Characterizations and Sheaf Representations of Regular and Weakly Regular Monoids and Semirings”, PhD Thesis, Quaid-I-Azam University, Pakistan, 1995.
G. Yesilot, K. Orel, U. Tekir, On prime subsemimodules of semimodules, Int. J. Algebra 4 (1) (2010), 53 – 60.