{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,5]],"date-time":"2024-04-05T11:36:07Z","timestamp":1712316967098},"reference-count":7,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2017,8]]},"abstract":"<jats:p> In this paper, we deal with the problem of computing the sum of the [Formula: see text]th powers of all the elements of the matrix ring [Formula: see text] with [Formula: see text] and [Formula: see text] a finite commutative ring. We completely solve the problem in the case [Formula: see text] and give some results that compute the value of this sum if [Formula: see text] is an arbitrary finite commutative ring for many values of [Formula: see text] and [Formula: see text]. Finally, based on computational evidence and using some technical results proved in this paper, we conjecture that the sum of the [Formula: see text]th powers of all the elements of the matrix ring [Formula: see text] is always [Formula: see text] unless [Formula: see text], [Formula: see text], [Formula: see text] and the only element [Formula: see text] such that [Formula: see text] is idempotent, in which case the sum is [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196717500278","type":"journal-article","created":{"date-parts":[[2017,7,10]],"date-time":"2017-07-10T10:53:01Z","timestamp":1499683981000},"page":"547-560","source":"Crossref","is-referenced-by-count":1,"title":["On power sums of matrices over a finite commutative ring"],"prefix":"10.1142","volume":"27","author":[{"given":"P.","family":"Fortuny","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad de Oviedo, Avda. Calvo Sotelo, s\/n, 33007 Oviedo, Spain"}]},{"given":"J. M.","family":"Grau","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad de Oviedo, Avda. Calvo Sotelo, s\/n, 33007 Oviedo, Spain"}]},{"given":"A. M.","family":"Oller-Marc\u00e9n","sequence":"additional","affiliation":[{"name":"Centro Universitario de la Defensa de zaragoza, Ctra. Huesca s\/n, 50090 Zaragoza, Spain"}]},{"given":"I. F.","family":"R\u00faa","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad de Oviedo, C\/ Federico Garc\u00eda Lorca 18, 33007 Oviedo, Spain"}]}],"member":"219","published-online":{"date-parts":[[2017,8,27]]},"reference":[{"key":"S0218196717500278BIB001","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-74-04102-7"},{"issue":"3","key":"S0218196717500278BIB003","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1007\/s00605-015-0736-5","volume":"178","author":"Fortuny P.","year":"2015","journal-title":"Monatsh. Math."},{"key":"S0218196717500278BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s00006-015-0544-y"},{"key":"S0218196717500278BIB005","doi-asserted-by":"publisher","DOI":"10.1002\/mana.201500057"},{"key":"S0218196717500278BIB006","doi-asserted-by":"publisher","DOI":"10.1007\/s00605-014-0660-0"},{"issue":"4","key":"S0218196717500278BIB007","first-page":"166","volume":"16","author":"Moree P.","year":"1994","journal-title":"C. R. Math. Rep. Acad. Sci. Canada"},{"key":"S0218196717500278BIB009","doi-asserted-by":"publisher","DOI":"10.1515\/crll.1840.21.372"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196717500278","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T16:42:55Z","timestamp":1565196175000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196717500278"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8]]},"references-count":7,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2017,8,27]]},"published-print":{"date-parts":[[2017,8]]}},"alternative-id":["10.1142\/S0218196717500278"],"URL":"https:\/\/doi.org\/10.1142\/s0218196717500278","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,8]]}}}