{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T12:56:42Z","timestamp":1762520202676,"version":"3.41.2"},"reference-count":37,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2025,8]]},"abstract":"<jats:p> Rota\u2013Baxter operators have been studied since 1960, and there are lots of their applications in mathematical physics, number theory, and noncommutative geometry. We state a surprisingly general property of such operators: the spectrum of every Rota\u2013Baxter operator of weight\u00a0[Formula: see text] on a\u00a0finite-dimensional unital (not necessarily associative) algebra is a\u00a0subset of [Formula: see text]. We even extend this result to the case of infinite-dimensional algebraic algebras (when [Formula: see text]). Based on these results, we define a new invariant of an algebra: the Rota\u2013Baxter [Formula: see text]-index [Formula: see text] of an algebra A as the infimum of the degrees of minimal polynomials of all Rota\u2013Baxter operators of weight\u00a0[Formula: see text] on\u00a0A. We compute the Rota\u2013Baxter [Formula: see text]-index for the matrix algebra [Formula: see text], [Formula: see text]: it is shown that [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196725500195","type":"journal-article","created":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T04:05:51Z","timestamp":1746763551000},"page":"687-712","source":"Crossref","is-referenced-by-count":1,"title":["Spectrum of Rota\u2013Baxter operators"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7839-5714","authenticated-orcid":false,"given":"Vsevolod","family":"Gubarev","sequence":"first","affiliation":[{"name":"Sobolev Institute of Mathematics, Acad. 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