{ "item_title" : "Module Theory", "item_author" : [" Alberto Facchini "], "item_description" : "This expository monograph was written for three reasons. Firstly, we wanted to present the solution to a problem posed by Wolfgang Krull in 1932Krull 32]. He asked whether what we now call the Krull-Schmidt Theorem holds for ar- tinian modules. The problem remained open for 63 years: its solution, a negative answer to Krull's question, was published only in 1995 (seeFacchini, Herbera, Levy and Vamos]). Secondly, we wanted to present the answer to a question posed by Warfield in 1975Warfield 75]. He proved that every finitely pre- sented module over a serial ring is a direct sum of uniserial modules, and asked if such a decomposition was unique. In other words, Warfield asked whether the Krull-Schmidt Theorem holds for serial modules. The solution to this problem, a negative answer again, appeared inFacchini 96]. Thirdly, the so- lution to Warfield's problem shows interesting behavior, a rare phenomenon in the history of Krull-Schmidt type theorems. Essentially, the Krull-Schmidt Theorem holds for some classes of modules and not for others. When it does hold, any two indecomposable decompositions are uniquely determined up to a permutation, and when it does not hold for a class of modules, this is proved via an example. For serial modules the Krull-Schmidt Theorem does not hold, but any two indecomposable decompositions are uniquely determined up to two permutations. We wanted to present such a phenomenon to a wider math- ematical audience.", "item_img_path" : "https://covers2.booksamillion.com/covers/bam/3/76/435/908/3764359080_b.jpg", "price_data" : { "retail_price" : "109.99", "online_price" : "109.99", "our_price" : "109.99", "club_price" : "109.99", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

Overview

Customers Also Bought

Details