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## τ-IRREDUCIBLE DIVISOR GRAPHS IN COMMUTATIVE RINGS WITH ZERO-DIVISORS

#### Christopher Park Mooney [1]

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In this paper, we combine research done recently in two areas of factorization theory. The first is the extension of τ-factorization to commutative rings with zero-divisors. The second is the extension of irreducible divisor graphs of elements from integral domains to commutative rings with zero-divisors. We introduce the τ-irreducible divisor graph for various choices of associate and irreducible. By using τ-irreducible divisor graphs, we find that we are able to obtain, as subcases, many of the graphs associated with commutative rings which followed from the landmark 1988 paper by I. Beck. We then are able to use these graphs to give alternative characterizations of τ-finite factorization properties previously defined in the literature.
Factorization, zero-divisors, commutative rings, zero-divisor graphs, irreducible divisor graphs
Konular Matematik JA99SE43RK Makaleler Yazar: Christopher Park Mooney
 Bibtex @ { ieja266183, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2016}, volume = {20}, pages = {45 - 69}, doi = {10.24330/ieja.266183}, title = {τ-IRREDUCIBLE DIVISOR GRAPHS IN COMMUTATIVE RINGS WITH ZERO-DIVISORS}, key = {cite}, author = {Mooney, Christopher Park} } APA Mooney, C . (2016). τ-IRREDUCIBLE DIVISOR GRAPHS IN COMMUTATIVE RINGS WITH ZERO-DIVISORS. International Electronic Journal of Algebra, 20 (20), 45-69. DOI: 10.24330/ieja.266183 MLA Mooney, C . "τ-IRREDUCIBLE DIVISOR GRAPHS IN COMMUTATIVE RINGS WITH ZERO-DIVISORS". International Electronic Journal of Algebra 20 (2016): 45-69 Chicago Mooney, C . "τ-IRREDUCIBLE DIVISOR GRAPHS IN COMMUTATIVE RINGS WITH ZERO-DIVISORS". International Electronic Journal of Algebra 20 (2016): 45-69 RIS TY - JOUR T1 - τ-IRREDUCIBLE DIVISOR GRAPHS IN COMMUTATIVE RINGS WITH ZERO-DIVISORS AU - Christopher Park Mooney Y1 - 2016 PY - 2016 N1 - doi: 10.24330/ieja.266183 DO - 10.24330/ieja.266183 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 45 EP - 69 VL - 20 IS - 20 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.266183 UR - http://dx.doi.org/10.24330/ieja.266183 Y2 - 2019 ER - EndNote %0 International Electronic Journal of Algebra τ-IRREDUCIBLE DIVISOR GRAPHS IN COMMUTATIVE RINGS WITH ZERO-DIVISORS %A Christopher Park Mooney %T τ-IRREDUCIBLE DIVISOR GRAPHS IN COMMUTATIVE RINGS WITH ZERO-DIVISORS %D 2016 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 20 %N 20 %R doi: 10.24330/ieja.266183 %U 10.24330/ieja.266183 ISNAD Mooney, Christopher Park . "τ-IRREDUCIBLE DIVISOR GRAPHS IN COMMUTATIVE RINGS WITH ZERO-DIVISORS". International Electronic Journal of Algebra 20 / 20 (Aralık 2016): 45-69. http://dx.doi.org/10.24330/ieja.266183