×
Louartiti, Khalid; Mahdou, Najib

Transfer of multiplication-like conditions in amalgamated algebra along an ideal. (English) Zbl 1277.13012

Afr. Diaspora J. Math. 14, No. 1, 119-125 (2012).
Summary: Let \(f:A\rightarrow B\) be a ring homomorphism and let \(J\) be an ideal of \(B\). In this paper, we study the multiplicationlike conditions in \(A\bowtie^fJ\).

Cited in 3 Documents

MSC:

13D05 Homological dimension and commutative rings
13D02 Syzygies, resolutions, complexes and commutative rings

Keywords:

multiplication ring; amalgamated algebras along an ideal
PDF BibTeX XML Cite
\textit{K. Louartiti} and \textit{N. Mahdou}, Afr. Diaspora J. Math. 14, No. 1, 119--125 (2012; Zbl 1277.13012)
Full Text: arXiv Euclid
  • logo of hbz
  • logo of WorldCat

References:

[1] D.D. Anderson; Commutative rings , in: Jim Brewer, Sarah Glaz, William Heinzer, Bruce Olberding (Eds.), Multiplicative Ideal Theory in Commutative Algebra: A tribute to the work of Robert Gilmer, Springer, New York, 2006, pp. 1-20. · Zbl 1115.13013
[2] D.D. Anderson; Multiplication Ideals, Multiplication rings, And the ring \(R(X)\) , Can. J. Math, 45 (4)1976, pp. 760-768. · Zbl 0343.13009
[3] M.B. Boisen and P.B. Sheldon; CPI-extension: Over rings of integral domains with special prime spectrum , Canad. J. Math. 29 (1977), 722-737. · Zbl 0363.13002
[4] M. Chhiti and N. Mahdou; Some homological properties of amalgamated duplication of a ring along an ideal , Bulletin of the Iranian Mathematical Society (to appear). · Zbl 1288.13013
[5] M.M. Ali and D. J. Smith; Generalized GCD Rings , Beitrage zur Algebra und Geometrie, Contributions to Algebra and Geometry, Auckland, New Zealand, 2001, No.1, pp. 219-233. · Zbl 0971.13002
[6] H.S. Butts and R.C. Phillips; Almost multiplication rings , Louisiana State University and Wofford College. (1963) · Zbl 0196.30901
[7] J.L. Dorroh; Concerning adjunctions to algebras , Bull. Amer. Math. Soc. 38 (1932), 85-88. · Zbl 0003.38701
[8] M. D’Anna, C. A. Finacchiaro, and M. Fontana; Amalgamated algebras along an ideal , Comm Algebra and Aplications, Walter De Gruyter (2009), 241-252.
[9] M. D’Anna, C. A. Finacchiaro, and M. Fontana; Properties of chains of prime ideals in amalgamated algebras along an ideal , J. Pure Applied Algebra 214 (2010), 1633-1641 · Zbl 1191.13006
[10] M. D’Anna; A construction of Gorenstein rings ; J. Algebra 306 (2) (2006), 507-519. · Zbl 1120.13022
[11] M. D’Anna and M. Fontana; The amalgamated duplication of a ring along a multiplicative-canonical ideal , Ark. Mat. 45 (2) (2007), 241-252. · Zbl 1143.13002
[12] M. D’Anna and M. Fontana; An amalgamated duplication of a ring along an ideal: the basic properties , J. Algebra Appl. 6 (3) (2007), 443-459. · Zbl 1126.13002
[13] M. Griffin; Multiplication rings via their total quotient rings , Can. J. Math. 26 (2) (1974), 430-449. · Zbl 0259.13007
[14] M. D. Larsen and P. J. McCarthy; Multiplicative Theory of Ideals , Academic Press New York and London. (1971). · Zbl 0237.13002
[15] J. L. Mott; Equivalent conditions for a ring to be a multiplication ring , Louisiana State University in May, 26 (2) (1963). · Zbl 0124.02201
[16] M. Nagata; Local Rings , Interscience, New York, 1962. · Zbl 0123.03402
[17] C. C. Weibel, An introduction to homological algebra , Cambridge University Press, United Kingdom, (1994). · Zbl 0797.18001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.