{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T16:02:15Z","timestamp":1773676935085,"version":"3.50.1"},"publisher-location":"Providence, Rhode Island","reference-count":24,"publisher":"American Mathematical Society","isbn-type":[{"value":"9781470481001","type":"print"},{"value":"9781470477639","type":"print"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025]]},"abstract":"<p>\n                    A ring with identity is called essentially right quasi-duo if every essential maximal right ideal of it is a two-sided ideal. Essentially right quasi-duo rings generalize essentially right duo rings, a notion that arose in the study of hypercyclic rings, and right quasi-duo rings, as introduced by S.H. Brown. We prove that a ring\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper R\">\n                        <mml:semantics>\n                          <mml:mi>R<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">R<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is essentially right quasi-duo if and only if\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper R\">\n                        <mml:semantics>\n                          <mml:mi>R<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">R<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is semisimple or\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper R slash upper S o c left-parenthesis upper R Subscript upper R Baseline right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>R<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo>\/<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:mi>S<\/mml:mi>\n                            <mml:mi>o<\/mml:mi>\n                            <mml:mi>c<\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:msub>\n                              <mml:mi>R<\/mml:mi>\n                              <mml:mi>R<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">R\/Soc(R_R)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is right quasi-duo. Although it is still unknown, whether a right quasi-duo ring is left quasi-duo, we provide an example of an essentially right quasi-duo ring that is not essentially left quasi-duo. Furthermore, while exchange right quasi-duo rings are known to be clean, there exist exchange essentially right quasi-duo rings that are not clean. A thorough study of essentially right quasi-duo rings is carried out and their relationship to skew power series rings, trivial extensions and formal triangular matrix rings is explored.\n                  <\/p>","DOI":"10.1090\/conm\/826\/16589","type":"other","created":{"date-parts":[[2025,9,22]],"date-time":"2025-09-22T15:27:13Z","timestamp":1758554833000},"page":"161-174","source":"Crossref","is-referenced-by-count":0,"title":["Essentially quasi-duo rings"],"prefix":"10.1090","author":[{"given":"Christian","family":"Lomp","sequence":"first","affiliation":[]},{"given":"Mohamed","family":"Yousif","sequence":"additional","affiliation":[]},{"given":"Yiqiang","family":"Zhou","sequence":"additional","affiliation":[]}],"member":"14","reference":[{"key":"1","doi-asserted-by":"publisher","first-page":"79","DOI":"10.2307\/1993133","article-title":"Properties of primary noncommutative rings","volume":"89","author":"Feller, Edmund H.","year":"1958","journal-title":"Trans. Amer. Math. 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