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Bibliographic Details
Main Authors:	Ke, Wen-Fong, Meyer, Johannes H.
Format:	Preprint
Published:	2024
Subjects:	Rings and Algebras 16Y30, 20E06, 20E32, 16N60, 16N80
Online Access:	https://arxiv.org/abs/2405.12597
Tags:	Add Tag No Tags, Be the first to tag this record!

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author	Ke, Wen-Fong Meyer, Johannes H.
author_facet	Ke, Wen-Fong Meyer, Johannes H.
contents	We show that there exist zero-symmetric simple nearrings with identity which are not equiprime, solving a longstanding open problem.
format	Preprint
id	arxiv_https___arxiv_org_abs_2405_12597
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Are zero-symmetric simple nearrings with identity equiprime? Ke, Wen-Fong Meyer, Johannes H. Rings and Algebras 16Y30, 20E06, 20E32, 16N60, 16N80 We show that there exist zero-symmetric simple nearrings with identity which are not equiprime, solving a longstanding open problem.
title	Are zero-symmetric simple nearrings with identity equiprime?
topic	Rings and Algebras 16Y30, 20E06, 20E32, 16N60, 16N80
url	https://arxiv.org/abs/2405.12597

if (filemtime($filename) + $maxlifetime < time()) { unlink($filename); $count++; } } return $count; } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ protected function saveSession($sessId, $data): bool { $sessFile = $this->path . '/sess_' . $sessId; if ($handle = fopen($sessFile, 'w')) { $return = false; // Lock the file for exclusive access to avoid issues with multiple // processes writing session simultaneously: if (flock($handle, LOCK_EX)) { $return = fwrite($handle, $data); // Make sure that there's no trailing data by truncating the file to // the correct length: ftruncate($handle, strlen($data)); fflush($handle); flock($handle, LOCK_UN); } fclose($handle); if ($return !== false) { return true; } } // If we got this far, something went wrong with the file output... // It is tempting to throw an exception here, but this code is called // outside of the context of exception handling, so all we can do is // echo a message.

// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

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